A为n阶矩阵,B为m阶矩阵,C为m×n矩阵,D为n×m矩阵,其中A和B可逆;证明:|A||D-CA^-1B|=|D||A-BD^-1C|
A为n阶矩阵,B为m阶矩阵,C为m×n矩阵,D为n×m矩阵,其中A和B可逆;证明:|A||D-CA^-1B|=|D||A-BD^-1C|
数学人气:161 ℃时间:2019-12-16 19:50:45
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是 A,D 可逆吧设H=A BC D一方面有E 0-CA^-1 E乘 H =A B0 D-CA^-1B所以 |H| = |A||D-CA^-1B|.另一方面 H 乘E 0-D^-1C E=A-BD^-1C B0 D所以 |H| = |D||A-BD^-1C|.综上有 |A||D-CA^-1B|=|D||A-BD^-1C|...
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