# Easy Skew-Symmetric problem

• February 10th 2011, 04:09 PM
fizzle45
Easy Skew-Symmetric problem
Hi here is my problem
$Let \mathbf{A}\text{ be an }n\,\times \,n\text{ skew-symmetric matrix and }\mathbf{x}\text{ be an }n\,\times\,1\text{ vector. Show that }\mathbf{x^TAx}=0 for all \mathbf{x}\in\mathbb{R}^n.$ my professor said it was a two line proof using A^T=-A and (AB)^T=B^T*A^T but with that information it seems like it is not enough. any help would be great.

i figured it out, now how do i delete this post?!
• February 10th 2011, 07:11 PM
tonio
Quote:

Originally Posted by fizzle45
Hi here is my problem
$Let \mathbf{A}\text{ be an }n\,\times \,n\text{ skew-symmetric matrix and }\mathbf{x}\text{ be an }n\,\times\,1\text{ vector. Show that }\mathbf{x^TAx}=0 for all \mathbf{x}\in\mathbb{R}^n.$ my professor said it was a two line proof using A^T=-A and (AB)^T=B^T*A^T but with that information it seems like it is not enough. any help would be great.

i figured it out, now how do i delete this post?!

$x^tAx=(xA^tx^t)^t=(-xA^tx^t)^t=-x^tAx$ ...

Tonio