→ itsart:了解! 謝謝~ 01/05 22:45
※ 引述《itsart (secret)》之銘言：
: 1.If B is similar to A and B is invertible, then A is invertible
: and A^-1 and B^-1 are similar
: 這題該怎麼證?
-1
B is invertible => B exists
-1
A and B are similar => there's exist P ,invertible, s.t. A=PBP
-1 -1 -1 -1 -1 -1 -1 -1
A(PB P ) = (PBP )(PB P ) = PBP PB P = I
-1 -1 -1 -1 -1 -1 -1 -1
and (PB P )A = (PB P )(PBP )= PB P PBP =I
-1 -1 -1 -1 -1
thus A =PB P , and so A and B are similar
: 2.If Ax=λx for some vector x,thenλ may be not an eigenvalue of A
: 答案為True,是因為x可能為0向量嗎
是的
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