线性代数-相似矩阵.pdf

文档介绍：1oÙ Ý
A¯K†ƒqéz
§4 ƒqÝ
Ý
éz
XJ•3Œ_Ý
P, ¦ P−1AP = Λ, ***@o
AP    
0 −1 −1 1 1 1
  r  
P = 0 −2 −2 → 0 −1 −1, P 6→ E, P ØŒ_.
   
1 1 1 0 0 0Ý
éz
n Ý
A Œéz ⇐⇒ P Œ_
⇐⇒ P →r E
⇐⇒ R(P) = n
⇐⇒ R(p1, p2, · · · , pn) = n
⇐⇒ p1, p2, · · · , pn ‚5Ã'
½n ()
n •
A Œéz ⇐⇒ A k n ‡‚5Ã'A•þ.ŒézÝ
íØ
XJ n •
A k n ‡pÉAŠ, K A Œéz.
~
 
−2 3 −3
 
A = −4 5 −3 AŠÚA•þ•g•
 
−4 4 −2
     
0 1 1
     
λ1 = 2, p1 = 1 ; λ2 = −2, p2 = 1 ; λ3 = 1, p3 = 1 .
     
1 1 0
 
2 0 0
−1  
P P = (p1, p2, p3), K P AP = 0 −2 0.
