
Matrix Symmetry Proof
I am to prove that if A is antisymmetric, then x^TAx = 0 for any column vector x. I know that by definition A^T = A, so (x^TAx) = (x^TAx). I have tried taking the transpose of both sides but this does not seem to help prove the above.
Any help would be appreciated.

Use that
so, it is symmetric.

Quote:
Originally Posted by
FernandoRevilla Use that
so, it is symmetric.
This completes the proof very nicely. However, how do I show formally that this is true?

xᵀ is 1xn, A is nxn, x is nx1, so Ax is nx1, so xᵀ(Ax) is 1x1 (it's just the inner product of x and Ax).