# Standard Matrix of Linear Transformation

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• Apr 4th 2012, 06:11 AM
renolovexoxo
Standard Matrix of Linear Transformation
Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.

I was able to get the standard matrix of a x x, but i dont really understand how to prove that it is skew symmetric. I can see it in this case, but in general I don't see a rule for it.
• Apr 4th 2012, 07:12 AM
Dinkydoe
Re: Standard Matrix of Linear Transformation
If you have the matrix A, I think it's quite clear that it's skew-symmetric. You only need to verify that \$\displaystyle A= -A^T\$.
• Apr 4th 2012, 08:24 AM
renolovexoxo
Re: Standard Matrix of Linear Transformation
I was just under the assumption that I needed to prove it for any A. I showed that for the case of the matrix I had. In class he started talking about proving it in general when I don't have the matrix A. That's where I'm getting stuck, is for all other possible matrices of cross products. Will they all be the same?
• Apr 4th 2012, 08:46 AM
Dinkydoe
Re: Standard Matrix of Linear Transformation
Ofcourse....u calculated A for a vector a=(x,y,z) right? Not for a chosen vector (1,2,4) for example. The matrix A is dependant on the vector a.

What is the matrix A u have?