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考研数学之线性代数知识点以及重要性质指导
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发表于 2010-08-25 20:45
楼主
[html]<
 style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">数学中，线性代数这门课程的概念多、定理多、符号多、运算规律多、内容相互纵横交错，知识前后紧密联系。下面就对线代每章中一些具体知识点以及重要性质作一阐述：</P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>一、行列式</B></P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">行列式的核心内容是求行列式，包括具体行列式的计算和抽象行列式的计算，其中具体行列式的计算又有低阶和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 15px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 16px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823125.gif"></SUB>阶两种类型。主要方法是应用行列式按行或者列展开定理和化为上下三角行列式求解，还可能用到的方法包括：行列式的定义（<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 13px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 15px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823126.gif"></SUB>阶行列式的值为取自不同行、不同列的<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 15px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 16px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image001.gif" name="AsyncWordImage"></SPAN></SUB>个元素的乘积的代数和）、性质<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 40px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823128.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823129.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 39px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823130.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 21px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823131.gif"></SUB>（其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823132.gif"></SUB>为矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 19px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823133.gif"></SUB>的特征值）、行列式的性质（如“数乘行列式等于用此数乘一行列式中的某一行或某一列”）。对于抽象行列式的求值，考点不在求行列式，而在于考虑<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823134.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 28px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823135.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 37px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823136.gif"></SUB>等的相关性质。</P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">二、矩阵</STRONG></P>< style="ADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">矩阵中除可逆阵、伴随阵、分块阵、初等阵等重要概念外，主要也是运算，其运算分两个层次，一是运用矩阵的性质对抽象矩阵进行运算，二是具体矩阵的数值运算。</P><P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">下面的表格分类列出了逆矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 29px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823137.gif"></SUB>、伴随矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823138.gif"></SUB>、矩阵转置<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 23px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image009.gif" name="AsyncWordImage"></SPAN></SUB>的性质以供区别记忆：</P> <table style="BORDER-COLLAPSE: collapse; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px" border=1 cellSpacing=0 cellPadding=0 width=550> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>行列式性质</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>特征值性质（<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 15px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823139.gif"></SUB>为矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823140.gif"></SUB>的特征值）</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>运算性质</P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" align=center>秩的性质</P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">转置矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823143.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 50px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823144.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 27px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823145.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 87px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823146.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 109px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823147.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 118px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823148.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 138px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823149.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 110px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823150.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 134px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823151.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823152.gif"></SUB></P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">逆矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823153.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 82px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 47px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823154.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 41px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823155.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">伴随矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823156.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 89px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823157.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 42px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823158.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823159.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823160.gif"></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 30px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image026.gif" name="AsyncWordImage"></SPAN></SUB>三者之间有一个既好记又好用的性质</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823161.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823162.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 113px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823163.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 163px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 75px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823164.gif"></SUB></P></td> </tr> <tr> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=66> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">数乘矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 30px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823165.gif"></SUB>、矩阵之积<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823166.gif"></SUB>及矩阵之和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 47px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823167.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=132> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 88px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823168.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 108px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823169.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=104> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 31px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823170.gif"></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823171.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 78px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823172.gif"></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 47px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823174.gif"></SUB></P></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=151></td> <td style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px" vAlign=top width=189> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823176.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823177.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823178.gif"></SUB>则有：<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 106px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823179.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 21px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823180.gif"></SUB>是可逆矩阵则有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 91px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823181.gif"></SUB>；同样，若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 16px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823182.gif"></SUB>可逆则有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 100px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823183.gif"></SUB></P></td> </tr> </table> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">三、向量、线性方程组</STRONG></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">向量与线性方程组的内容联系很密切，很多知识点相互之间都有或明或暗的相关性。复习这两章最有效的方法就是彻底弄清楚诸多知识点之间的内在联系，因为这样做首先能够保证做到真正意义上的理解，同时也是熟练掌握和灵活运用的前提。以下给出这部分主要知识点：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">三个双重定义：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.秩的定义</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a.矩阵秩的定义：矩阵中非零子式的最高阶数。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b.向量组秩定义：向量组的极大线性无关组中的向量个数。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.线性相关无关的定义</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a. 对于一组向量<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 95px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823184.gif"></SUB>，若存在不全为零的数<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 82px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823185.gif">使得<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 201px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823186.gif">成立，则相量组线性相关，否则向量组线性无关，即上述等式当且仅当<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823187.gif">全为0时才成立。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b. 向量组<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 94px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 30px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823188.gif">线性相关ó向量组中至少存在一个向量可由其余<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 15px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 16px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image001.gif" name="AsyncWordImage"></SPAN>-1个向量线性表出；线性无关ó向量组中没有一个向量可由其余的向量线性表出。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">3．线性方程组的两种形式</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">a. 矩阵形式：<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823189.gif"></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">b. 向量形式：<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 232px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823190.gif"></SUB></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>两条性质：</B></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.对于方阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 42px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823191.gif"></SUB>有：方阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823192.gif"></SUB>可逆ó存在方阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823194.gif"></SUB>使得<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 110px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823195.gif"></SUB>ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 59px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823196.gif"></SUB>ó<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN></SUB>的行列向量组均线性无关ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 74px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823197.gif"></SUB>ó<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 69px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823198.gif"></SUB>可由克莱姆法则判断有唯一解，而<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 54px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823199.gif"></SUB>仅有零解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">对于一般矩阵<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 42px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 27px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image062.gif" name="AsyncWordImage"></SPAN>则有：<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 72px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823200.gif">ó<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量组线性无关ó<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 54px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image069.gif" name="AsyncWordImage"></SPAN>仅有零解，<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 56px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823201.gif">有唯一解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.齐次线性方程组<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 54px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image069.gif" name="AsyncWordImage"></SPAN>是否有非零解对应于系数矩阵<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量组是否线性相关，而非齐次线性方程组<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 56px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image071.gif" name="AsyncWordImage"></SPAN>是否有解对应于<IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 19px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823202.gif">是否可以由<SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image063.gif" name="AsyncWordImage"></SPAN>的列向量组线性表出。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">以上两条性质可视为是将线性相关、行列式、秩、线性方程组几部分知识联系在一起的桥梁。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><B>关于秩的一些结论</B>：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 145px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823203.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 149px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823204.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 177px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823205.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 178px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823206.gif"></SUB>；<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 174px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823207.gif"></SUB>；若有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 35px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823208.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 32px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823209.gif"></SUB>满足<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 51px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823210.gif"></SUB>，则<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 103px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823211.gif"></SUB>；若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823212.gif"></SUB>是可逆矩阵，则有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 99px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823213.gif"></SUB>；同样若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823214.gif"></SUB>可逆则有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 98px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823215.gif"></SUB>。非齐次线性方程组<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 61px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823216.gif"></SUB>有唯一解则对应齐次方程组<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 58px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823217.gif"></SUB>仅有零解，若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 53px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823218.gif"></SUB>有无穷多解则<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 58px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image087.gif" name="AsyncWordImage"></SPAN></SUB>有非零解；若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 69px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image068.gif" name="AsyncWordImage"></SPAN></SUB>有两个不同的解则<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 58px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image087.gif" name="AsyncWordImage"></SPAN></SUB>有非零解；若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 17px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 19px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image015.gif" name="AsyncWordImage"></SPAN></SUB>是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 46px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823219.gif"></SUB>矩阵而<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 80px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823220.gif"></SUB>则<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 59px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823221.gif"></SUB>一定有解，而且当<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 49px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 17px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823222.gif"></SUB>时是唯一解，当<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 52px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823223.gif"></SUB>时是无穷多解，而若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 70px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823224.gif"></SUB>则<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 51px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 19px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823225.gif"></SUB>没有解或有唯一解。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px"><STRONG style="FONT-STYLE: normal; FONT-WEIGHT: 800">四、特征值与特征向量</STRONG></P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">本章知识要点如下：</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">1.特征值和特征向量的定义及计算方法就是记牢一系列公式，如:<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 62px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823226.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 49px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823227.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 86px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823228.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 103px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823229.gif"></SUB>和<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 98px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823230.gif"></SUB>。在历年真题中常用到下列性质：若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 20px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823231.gif"></SUB>阶矩阵<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823232.gif"></SUB>有<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 18px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 20px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image101.gif" name="AsyncWordImage"></SPAN></SUB>个特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823233.gif"></SUB><SPAN class=Apple-converted-space> </SPAN><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 44px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823235.gif"></SUB><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823237.gif"></SUB>，则有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 120px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823238.gif"></SUB>；若矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 17px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 19px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image015.gif" name="AsyncWordImage"></SPAN></SUB>有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 20px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 26px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823239.gif"></SUB>，则<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 23px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 21px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823240.gif"></SUB>、<B><SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823241.gif"></SUB></B>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 68px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823242.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 43px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823243.gif"></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 30px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 23px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image026.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823244.gif"></SUB>分别有特征值<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823245.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 29px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823246.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 54px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823247.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 41px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823248.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 47px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823249.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 32px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 45px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823250.gif"></SUB>，且对应特征向量等于<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 25px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 33px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823252.gif"></SUB>所对应的特征向量，而若<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 24px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 32px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823253.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 26px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 32px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823254.gif"></SUB>分别为矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>的特征值，则<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 52px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 28px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823256.gif"></SUB>不一定为<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 38px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823257.gif"></SUB>的特征值。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">2.相似矩阵及其性质。定义式为<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 88px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823258.gif"></SUB>，需要区分矩阵的相似、等价与合同：矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>与矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>等价的定义式是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 79px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823259.gif"></SUB>，其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 18px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823260.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 18px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823261.gif"></SUB>为可逆矩阵，此时矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>可通过初等变换化为矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 20px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image084.gif" name="AsyncWordImage"></SPAN></SUB>，并有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 81px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 22px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823262.gif"></SUB>；当<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 74px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823263.gif"></SUB>中的<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image126.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 17px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 23px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823264.gif"></SUB>互逆时就变成了矩阵相似的定义式，即有<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 90px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823265.gif"></SUB>，此时满足<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 93px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823266.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 68px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 25px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823267.gif"></SUB>、<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 164px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 27px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823268.gif"></SUB>，并且<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>、<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 20px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 21px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image084.gif" name="AsyncWordImage"></SPAN></SUB>有相同的特征值。矩阵合同的定义是<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 85px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 24px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823269.gif"></SUB>，其中<SUB><IMG style="BORDER-RIGHT-WIDTH: 0px; WIDTH: 22px; BORDER-TOP-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; HEIGHT: 15px; BORDER-LEFT-WIDTH: 0px" alt="考研数学线代部分复习指导 " src="http://img1.gtimg.com/edu/pics/29823/29823270.gif"></SUB>为可逆矩阵。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">由以上定义可看出等价、合同、相似三者之间的关系：若<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>与<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>合同或相似则<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>与<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 16px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 17px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image053.gif" name="AsyncWordImage"></SPAN></SUB>必等价，反之不成立；合同与等价之间没有必然联系。</P> <P style="PADDING-BOTTOM: 0px; LINE-HEIGHT: 25px; TEXT-INDENT: 2em; MARGIN: 20px auto 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; PADDING-TOP: 0px">3.矩阵可相似对角化的条件。包括两个充要条件和两个充分条件，充要条件（1）是<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 13px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 15px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image002.gif" name="AsyncWordImage"></SPAN></SUB>阶矩阵<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER-LEFT: rgb(118,118,118) 1px solid; WIDTH: 22px; BACKGROUND-REPEAT: no-repeat; BACKGROUND-POSITION: 50% 50%; HEIGHT: 18px; FONT-SIZE: 1px; BORDER-TOP: rgb(118,118,118) 1px solid; BORDER-RIGHT: rgb(118,118,118) 1px solid" imgkey="image102.gif" name="AsyncWordImage"></SPAN></SUB>有<SUB><SPAN style="BACKGROUND-IMAGE: url(http://edu.qq.com/tcms/images/loading.gif); BORDER-BOTTOM: rgb(118,118,118) 1px solid; BORDER- |
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