复习笔记Day5

2022-08-26 18:32 作者:臥煙鈴 0人读过 | 我要投稿

很抱歉今天只能带来一道题了，因为今天要收拾东西，快开学了不是吗，如果有错误的话也欢迎大家指正，谢谢大家了

10.(中山大学2016)

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$%E8%80%8C%E5%AF%B9%E4%BA%8E%5Cforall%20A%5Cin%20M_n(%5Cmathbb%7BC%7D)$

$%E8%AE%BE(E_%7B1%2C1%7D%2CE_%7B1%2C2%7D%2C%5Cldots%2CE_%7Bn%2Cn%7D)%5Calpha%5ET%3DA$

$A%5E*%3D(E_%7B1%2C1%7D%2CE_%7B1%2C2%7D%2C%5Cldots%2CE_%7Bn%2Cn%7D)U%5Calpha%5E*$

$%5Cvarphi%20(A%5E*)%3D(D_%7B1%2C1%7D%2CD_%7B1%2C2%7D%2C%5Cldots%2CD_%7Bk%2Ck%7D)FU%5Calpha%5E*$

$%3D(D_%7B1%2C1%7D%2CD_%7B1%2C2%7D%2C%5Cldots%2CD_%7Bk%2Ck%7D)P%5Coverline%20FUU%5Calpha%5E*$

$%3D(D_%7B1%2C1%7D%2CD_%7B1%2C2%7D%2C%5Cldots%2CD_%7Bk%2Ck%7D)P%5Coverline%20F%5Calpha%5E*$

$%5Cvarphi%20(A)%5ET%3D%5Ctau(%5Cvarphi%20(A))%3D(D_%7B1%2C1%7D%2CD_%7B1%2C2%7D%2C%5Cldots%2CD_%7Bk%2Ck%7D)PF%5Calpha%5ET$

$%5Cvarphi%20(A)%5E*%3D%5Coverline%5Ctau(%5Cvarphi%20(A))%3D(D_%7B1%2C1%7D%2CD_%7B1%2C2%7D%2C%5Cldots%2CD_%7Bk%2Ck%7D)P%5Coverline%20F%5Calpha%5E*$

$%3D%5Cvarphi%20(A%5E*)$

$%E6%95%85%5Cvarphi%20(A)%5E*%3D%5Cvarphi%20(A%5E*)%E6%88%90%E7%AB%8B%0A$

$%5Cmathbb%7BQ.E.D%7D$

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