Matrix

👨🏻‍🏫 學術台數學

[匿名]

2011-10-30 3:44 pm

A is a 3 x 3 square matrix. If det ( I - A) = 0 and (I - A) transpose = A - I, prove that det ( I - A^4) = 0.

更新1:

To : 自由自在 (I - A)^T = A - I provided is to make sure that there is no ambiguity in the type of matrix A, I am not sure if det(I - A^4) is true for all type of matrix.

回答 (2)

用戶25975

2011-10-30 5:55 pm

✔ 最佳答案

det (I - A4) = det [(I - A)(I + A)(I + A2)]

= det (I - A) x det (I + A) x det (I + A2)

= 0

參考: 原創答案

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用戶9112

2011-10-30 7:39 pm

I do not understand why need the condition (I - A)^T = A - I. Does not seem to be required in the analysis.

2011-10-30 12:06:30 補充：
I guess 將軍has proved this is true...

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