Prove that if $A$ is an $n\times n$ matrix, then $A - A^T$ is a skew-symmetric matrix.
Thank you!
Skew-symmetric matrices
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$\begingroup$
linear-algebra
matrices
transpose
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0Just to satisfy my curiosity: what does using the whole long method where I shall use a matrix mean? – 2017-01-29
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0Just take the transpose of the thing and see what you get. – 2017-01-29
1 Answers
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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.