A is a symmetric matrix. B is a asymmetric matrix. Is it true that
AB + (BA)^T = 0 ? Please prove.
Matrix
2014-06-29 7:56 pm
回答 (2)
2014-06-29 11:51 pm
2014-06-30 12:06 am
Remark:
If A is symmetric and B is skew-symmetric, then it is true that
AB + (BA)^T = 0.
Note that the properties in this case are:
A^T = A
B^T = -B
Thus,
AB + (BA)^T = AB + A^TB^T = AB + A(-B) = AB - AB = 0
2014-06-29 16:07:22 補充：
Asymmetric simply means not symmetric, not necessarily skew-symmetric, so 自由自在 知識長 is definitely correct!
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│ .✪‿✪ │
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If A is symmetric and B is skew-symmetric, then it is true that
AB + (BA)^T = 0.
Note that the properties in this case are:
A^T = A
B^T = -B
Thus,
AB + (BA)^T = AB + A^TB^T = AB + A(-B) = AB - AB = 0
2014-06-29 16:07:22 補充：
Asymmetric simply means not symmetric, not necessarily skew-symmetric, so 自由自在 知識長 is definitely correct!
╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯
收錄日期: 2021-04-23 23:25:42
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140629000051KK00050