# Easy Skew-Symmetric problem

• Feb 10th 2011, 04:09 PM
fizzle45
Easy Skew-Symmetric problem
Hi here is my problem
$\displaystyle Let$\mathbf{A}\text{ be an }n\,$$\times \,n$$\text{ skew-symmetric matrix and }\mathbf{x}\text{ be an }n\,$$\times$$\,1$$\text{ vector. Show that }\mathbf{x^TAx}=0 for all \mathbf{x}\in\mathbb{R}^n. my professor said it was a two line proof using A^T=-A and (AB)^T=B^T*A^T but with that information it seems like it is not enough. any help would be great. i figured it out, now how do i delete this post?! • Feb 10th 2011, 07:11 PM tonio Quote: Originally Posted by fizzle45 Hi here is my problem \displaystyle Let \mathbf{A}\text{ be an }n\,$$\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?!

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

Tonio