Re: [理工] [線代]-判斷相似

[itsforte ( )]

※ 引述《GI9 (   )》之銘言：
: Let A and B be two nxn matrices over C . Suppose that the 2nx2n matrix
: [A 0]                  [B 0]
: [0 A]    is similar to [0 B]
: Show that A is similar to B

我有問題...

M=[A 0]      N=[B 0]
  [0 A]        [0 B]

A特徵值:入a1 入a2...  　　　　　B特徵植:入b1 入b2...

M特徵值:入a1 入a1 入a2 入a2...  N特徵值:入b1 入b1 入b2 入b2...

A B不相似

M N光是特徵值就不一樣了

怎麼可能相似　~_~?


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◆ From: 140.113.139.124
※ 編輯: itsforte        來自: 140.113.139.124      (12/17 18:08)
推 polomoss:這是什麼所的線代阿~~我都不會@@
→ iyenn:你不能先假設ka1 kb1不同呀,如果相同就ok不是?
推 GI9:那你可以舉得出M、N相似 結果A、B不相似的例子嗎？
推 kkman0120:這數延所的嗎?
→ itsforte:我腦包看錯題目了 = =||
assume  A= p J p^(-1),   B= q K q^(-1), which A is NOT similar to B

[A 0] = [p J p^(-1)   0       ] = [p 0] [J 0] [p^(-1) 0     ]
[0 A]   [  0        p J p^(-1)]   [0 p] [0 J] [0      p^(-1)]

      = P [J 0] P^(-1)
          [0 J]

[B 0] = [q K q^(-1)   0       ] = [q 0] [K 0] [q^(-1) 0     ]
[0 B]   [  0        q K q^(-1)]   [0 q] [0 K] [0      q^(-1)]

      = Q [K 0] Q^(-1)
          [0 K]

=> [A 0] is not similar to [B 0]
   [0 A]                   [0 B]

<=> [A 0] is similar to [B 0]  => A is similar to B
    [0 A]               [0 B]
※ 編輯: itsforte        來自: 140.113.139.124      (12/18 13:49)