﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:trackback="http://madskills.com/public/xml/rss/module/trackback/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/"><channel><title>语源科技BlogJava-liming</title><link>http://www.blogjava.net/liming/</link><description /><language>zh-cn</language><lastBuildDate>Thu, 07 May 2026 07:22:21 GMT</lastBuildDate><pubDate>Thu, 07 May 2026 07:22:21 GMT</pubDate><ttl>60</ttl><item><title>矩阵特征向量和特征值的由来</title><link>http://www.blogjava.net/liming/archive/2008/12/28/248749.html</link><dc:creator>小老虎</dc:creator><author>小老虎</author><pubDate>Sun, 28 Dec 2008 08:06:00 GMT</pubDate><guid>http://www.blogjava.net/liming/archive/2008/12/28/248749.html</guid><wfw:comment>http://www.blogjava.net/liming/comments/248749.html</wfw:comment><comments>http://www.blogjava.net/liming/archive/2008/12/28/248749.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://www.blogjava.net/liming/comments/commentRss/248749.html</wfw:commentRss><trackback:ping>http://www.blogjava.net/liming/services/trackbacks/248749.html</trackback:ping><description><![CDATA[<p align="justify">&nbsp;</p>
<div class="Section0" style="layout-grid:  15.6pt none"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">解微分方程组</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">例（1）</font></span><span><img height="55" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image1.wmf" width="98"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt; text-align: justify"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">方法直接求解</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">（2）解如下微分方程组</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="55" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image2.wmf" width="281"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">因为（1）/&nbsp;(2)方程中就有既有x1，又有x2，我们想用一种变换使之成为例一的形式</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">令</font></span><span><img height="50" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image3.wmf" width="125"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">即Y=PX,&nbsp;X=P</font></span><span style="font-size: 10.5pt; vertical-align: super; font-family: '宋体'; mso-spacerun: 'yes'">-1</span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'">Y</span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image4.wmf" width="71"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">原方程变为</font></span><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image5.wmf" width="97"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image6.wmf" width="85"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">此时方程应为</font></span><span><img height="55" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image7.wmf" width="98"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">令</font></span><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image8.wmf" width="73"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">为</font></span><span><img height="74" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image9.wmf" width="74"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">的形式</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">令</font></span><span><img height="23" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image10.wmf" width="53"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="21" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image11.wmf" width="66"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">，</font></span><span><img height="23" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image12.wmf" width="119"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">，</font></span><span><img height="74" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image13.wmf" width="133"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="98" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image14.wmf" width="310"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="23" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image15.wmf" width="263"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">即为</font></span><span><img height="71" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image16.wmf" width="85"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">就是求解方程</font></span><span><img height="21" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image17.wmf" width="65"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">这就和大多数线性代数课本对应起来了</font></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">求解A</font></span><span style="font-size: 10.5pt; vertical-align: super; font-family: '宋体'; mso-spacerun: 'yes'">n</span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><font face="宋体">的需要</font></span><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image8.wmf" width="73"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'">=&gt;</span><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image18.wmf" width="74"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
<p class="p0" style="margin-top: 0pt; margin-bottom: 0pt"><span><img height="19" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/ksohtml/wps_clip_image19.wmf" width="247"  alt="" /></span><span style="font-size: 10.5pt; font-family: '宋体'; mso-spacerun: 'yes'"><o:p></o:p></span></p>
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