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Math Help - Standard Matrix of Linear Transformation

  1. #1
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    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.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    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 A= -A^T.
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  3. #3
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    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?
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  4. #4
    Senior Member Dinkydoe's Avatar
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    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?
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