计算方法之计算矩阵的特征值和特征量

1、0212222111211 nnnnnnaaaaaaaaa 3113A01)3(31132 EA043114321 xx0111121 xx21212100 xxxxxx 111P)0(1 kPk023112321 xx0111121 xx21212100 xxxxxx 112P)0(2 kPkini 1maxini 1min)()1(1limkjkjkvv )1( kjv)1( kV TnvvvV)0()0(2)0(1)0( nknkkkkXAXAXAVAV 1212111)0(1)1( nknnkkXXX 121221111 1211111ikniiikXX 21111)(ikniiikk

2、XXV )()(1211111)1(jikniiijkkjXXv )()(21111)(jikniiijkkjXXv )()()()(limlim211111211111)()1(jikniiijkjikniiijkkkjkjkXXXXvv 11 i0, 0111 kiki 1)()1(lim kjkjkvv)()1(1kjkjvv nvvnjkjkj 1)()1(1 1)()1(lim kjkjkvv)(1)1(kkVV )()1(kkAVV )(1)(kkVAV 1110A 11)0(V 21111110)0()1(AVV 32211110)1()2(AVV 53321110)2()3(A

3、VV 233144)10()11(AVV 3772332331441110)11()12(AVV61803. 123337761805. 1144233)11(2)12(21)11(1)12(11 VVVV 或者或者261803. 161805. 11 或或者者nknkkkkXAXAXAVAV 2211)0()(nknnkkXXX 222111)1(3122111ikniiikkXXX )1(22111)(XXVkkk )1(2221121)2(XXVkkk )(21kV )()2(1kikiVV )1()1(2211111)1(22111)(XXVXXVkkkkkk 22111)(1)1(1

4、111)(1)1(2)1(2XVVXVVkkkkkkk )(1)1(2)(1)1(1kkkkVVXVVX 11111211111)1(XXXVkikniiikk 11121111)(XXXVkikniiikk )0()0()1()1()1(AVAVVVU )0()0(2)1()2(AVVAAUV )0(2)0(2)2()2()2(VAVAVVUV(3) ： )0(2)0(3)2()3(VAVAAUV： )0()0()()()(VAVAVVUkkkkk )0()0(1)()1(VAVAAUVkkkk )()1()()()()0(kkkkkAUVVVUV取初值取初值)(11)( kXXUk当当 2

5、111121111)0()0()(ikniikikniikkkkXXXXVAVAU 211111211111)0()0(1)1(ikniikikniikkkkXXXXVAVAV 11XX。)(1 k当当 90688465441356133A ikniikikniikkXXXXV211111211111)1( )(lim)(1 kkV )(kiV)()1(kkAVV 121)1(1, kikiUV )(1)1(2)(1)1(1kkkkVVXVVX )1()1(13122111111312211111)1(ikniikkikniikkkXXXXXXU )1()1(22111112211111XXX

6、Xkkkk )1()()1( kkkAUAAVV )1()1(2211111222112111XXXAXAkkkk 21)1()1( kkUV121)1(1, kikiUV )1()1(221111122221121111XXXXkkkk iiiAX1X1 i 1, 1 , 0,UVV/VU)(1)1()()()( kAkkkkk, 1 , 0,UVV/VU)()1()()()( kAkkkkk 0235A 5/63515/21A )0(2)0(12115/21UUyy 21)1(2)1(15/635yyVV nTAPPAPP211kkTTTkTkkPPPAPPPPPA121121)1( 22

7、211211aaaaA2112aa 212221121121222221122111212),(xxaaaaxxxaxxaxaxxf 2121cossinsincosyyxx yyxyyxcossinsincos21221122111222tgaaa 2222211121),(ybybyyf 21222112112121222112112121cossinsincoscossinsincos),(yyaaaayyxxaaaaxxxxf),(),(2121yyfxxf 22112221121100cossinsincoscossinsincosbbaaaa Pcossinsincos 22110

8、0bbB 3113A Pcossinsincos APPTcossin23cossincossincossin23cossinsincos3113cossinsincos2222 2004,22cossinAPPBT 22222222cossinsincosP 2222 2222行行行行qpqpV 1cossin11sincos1),(nnijTaAVVA )()1()1( qpjiaaaaaaaaaqpiaaaaaaaaaaaaaaaajiijjiijppqqpqqppqiqipqiiqiqippiippqqqppqqpqqqpppp,2sin22cos,cossinsincos2sincossin2sinsincos)1()1()1()1()1()1()1()1(22)1(22)1(02sin22cos aaappqqpq0)1()1( qppqaa ninikpqkiikiinjinjikpqkijkijaaajiaaa112)(2)(2)1(1,1,2)(2)(2)1()(2)()()()(2)()()()(1,2)(jianji