If $A$ and $B$ are symmetric matrices of same order then $AB+BA$ must be symmetric. But my question is what will happen for $AB-BA$. Is $AB-BA$ symmetric or skew-symmetric or is there no conclusion?
Is $AB-BA$ symmetric or skew-symmetric?
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matrices
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0I think it is skew-symmetric – 2017-01-07
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0Just check the definition of skew symmetry. What do you get? – 2017-01-07
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1(AB-BA)^t=B^t A^t-A^t B^t=BA-AB=-(AB-BA) that implies it is skew-symmetric – 2017-01-07
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0yepp. Looks good. – 2017-01-07
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0Now I have another question transpose of symmetric matrix need not be symmetric matrix..plz explin me...clearly – 2017-01-07
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0again, check the definition. It is something you always try first. – 2017-01-07
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0a matrix A is symmetric if A^t=A.(A^t)^t=A=A^t..that implies transpose of symmetric matrix is symmetric – 2017-01-07
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0yes. looks good – 2017-01-07