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

$\displaystyle x^tAx\in \mathbb{R}^{1\times 1}$

so, it is symmetric.

Quote:

---

Originally Posted by FernandoRevilla

Use that

$\displaystyle x^tAx\in \mathbb{R}^{1\times 1}$

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).