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Math Help - Easy Skew-Symmetric problem

  1. #1
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    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?!
    Last edited by fizzle45; February 10th 2011 at 07:09 PM.
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  2. #2
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    Quote Originally Posted by fizzle45 View Post
    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
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