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