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1、Cayley-Hamilton½n©¬Schurnz½n111nnnÙÙÙAAAÝÝÝJordanIIIOOO///5CAA...¯ÌSchurnz½nµz{ÝÄ:IKJJII"ÛJI116£¶w«'4òÑ1Cayley-Hamilton½nCayley-Hamilton½n©¬Schurnz½n5CAA...ÝAAõªf(λ)§Kkf(A)=0"£y²:µ©¬Schurnz½n"¤¯Ìé?¿g,êm§kAm∈span{I,A,A2,···,An−1}"ùÒ
2、Jø«OIKpgü{"JJIIJI1.1.Sylvesterüüüúúúªªª126AB©O´m×nn×mݧm≥n§K
3、λI−AB
4、=λm−n
5、λI−mn£BA
6、"£y²:µ/qÝAÓ0/©¬Ý0"¤¶w«'4òÑ1.2."""zzzõõõªªªõõõªªª½ÂµA´nݧf(x)´õª"XJf(A)=0§K¡f(x)´A"zõª"gê$Ä"zõª¡Aõª§PmA(x)½m(x)"Cayley-Hamilton½n5µ©¬Schurnz½n•m(x)´Aõª
7、§f(x)´A?¿"zõª§5CAA...Km(x)f(x)"AO/§m(x)
8、xI−A
9、"£õª´¤k"zõªúÏf"¤£y²:µõªØ{"¤¯Ì•A´?¿§m(x)´Aõª§λ0∈C"Kλ0´AAIK⇐⇒m(λ0)=0"JJII•©¬éÝõªuf¬õªúª"£©¬éÝAõªuf¬Aõª¦JIÈ"¤136•qÝäkÓõª"£y²:µÝAB£q§f(x)õª§Kf(A)=0⇐⇒f(B)=0"¤¶w«•ÝA±éz⇐⇒ÝAõªvk"£
10、y²:µ'4©¬Schurnz½n£é©¬ê¤8B{"¤òÑ•A§f(x)´ÃϪõª"ef(A)=0§KA±éz"£Ïd§ÝéÜÝþéz"¤1.3.555CCCAAAAAAþþþCayley-Hamilton½n©¬Schurnz½nV´Cþ5m§σ∈EndV,λ∈C"XJ3"þα∈V¦5CAA...σ(α)=λα§K¡λ´σA§α´σ£áuAλ¤Aþ"XJλ´σA§KVf8Ü{x∈V:σ(x)=λx}¡σ£áuA¯Ìλ¤Af
11、m§PVλ"IKJJIIV´k5m§σ∈EndV§A´σ3,
12、ÄeݧKJI•AσkÓA¶146•PσLØÓAλ1,···,λs§KA±éz⇐⇒V=£sPi=1LVλi"u´§A±éz⇐⇒σ±éz§=σ=¶w«si=1σi§Ù¥§σi´σ3Vλiþ"'4òÑ2©¬Schurnz½nQnEÝAAõª
13、λI−A
14、=s(λ−λ)ni§Ù¥σ(A)={λ:Pi=1iisCayley-Hamilton½n1≤i≤s},i=1ni=n§K3_ÝP§¦©¬Schurn
15、z½nMMM5CAA...−1PAP=A1A2···As,Ù¥Ai´AþλiniþnÝ"¯ÌIK©¬Schurnz½ny²µJJII•£jnz½n¤A´nEݧK3jÝU§¦JI∗UAU=B,156Ù¥§BþnÝ"£y²:µ8B{"¤£•A=(aij)´Fþ?¿þnݧ1≤p16、᧦bpq=0"Cayley-Hamilton½n©¬Schurnz½n5CAA...¯ÌIKThankyou!JJIIJI166InstituteofStructuralMechanics,CAEP,P.O.BoxAddress:919-414,Mianyang,Sichuan,China,621900£E_mail:qlx1205@263.net&qian_lixin@sohu.com¶w«08162485474(O),08162482055(H),'4Tel:13981148
17、905(M)òÑFax:08162281485