Prove that if $A$ is an $n\times n$ matrix, then $A - A^T$ is a skew-symmetric matrix.

Thank you!


closed as off-topic by C. Falcon, TastyRomeo, Davide Giraudo, Shailesh, Behrouz Maleki Jan 29 '17 at 15:18

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  • $\begingroup$ Just to satisfy my curiosity: what does using the whole long method where I shall use a matrix mean? $\endgroup$ – TheGeekGreek Jan 29 '17 at 12:53
  • $\begingroup$ Just take the transpose of the thing and see what you get. $\endgroup$ – Oscar Lanzi Jan 29 '17 at 13:07

Skew symmetric means that $A^t = -A$. So in your case $$(A - A^t)^t = A^t - (A^t)^t = A^t - A = -(A - A^t)$$ since the operation of transposition is linear and involutory.


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