A and B are m x m matrix.
AB = BA = 0
Is it true that (A + B)^n = A^n + B^n ?
Please prove.
Matrix
2014-06-29 6:22 pm
回答 (3)
2014-06-29 6:53 pm
✔ 最佳答案
True.By expanding the term on LHS,
we can have terms A^n +nC1 A^(n-1) B+...+b^n
For the terms in the middle, they must have AB or BA, which are equal to 0.
Therefore, all the terms are zero except the first and last terms.
The answer is then A^n+B^n
參考: Me 2014 dse
2014-07-03 10:53 pm
I agree with cat cat as the question requires you to prove it.
So, mathematical induction is more convincing.
So, mathematical induction is more convincing.
2014-06-29 6:49 pm
True.
Please read:
圖片參考：https://s.yimg.com/rk/HA00430218/o/655125844.png
2014-07-03 11:24:59 補充：
No offence.
The proof is understandable but it is not rigorous in a mathematical sense.
Please read:
圖片參考：https://s.yimg.com/rk/HA00430218/o/655125844.png
2014-07-03 11:24:59 補充：
No offence.
The proof is understandable but it is not rigorous in a mathematical sense.
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原文連結 [永久失效]:
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