[理工] [线代]-反矩阵

楼主: Gojosatoru ( Gojosatoru)   2021-03-04 13:18:42
请问这个定理要怎么用数学归纳法证明呢?
一直搞不清楚要用一般的数学归纳法还是强数学归纳法证明,
还有是要从k=1还是k=2开始证明呢?
先谢谢大家了
定理:https://i.imgur.com/8InU9wW.png
作者: zamperla (地鼠王)   2021-03-04 15:38:00
A1*A2*...Ak is invertible(A1*A2*...Ak)(A1*A2*...Ak)^-1 = I(A2*A3*...Ak)(A1*A2*...Ak)^-1 = A^-1l(A3*A4*...Ak)(A1*A2*...Ak)^-1 = A^-2*A^-1I...(A1*A2*...Ak)^-1 = Ak^-1*...A1^-1

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