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Math Help - tricky matrix problem--please help!

  1. #1
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    tricky matrix problem--please help!

    Hi, I'm trying to solve the following problem:


    "Solve
    XA=Bfor A using matrix algebra, where Bis a n x 1
    vector,
    X is a n x k matrix, and A is a k x 1 vector. You can assume that

    any square matrices that you encounter have full rank."

    Usually this could be solved easily just by multiplying by the inverse of X, but since X is not a square matrix, I don't know what to do.

    Thanks!
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  2. #2
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    Quote Originally Posted by willis View Post
    Hi, I'm trying to solve the following problem:


    "Solve
    XA=Bfor A using matrix algebra, where Bis a n x 1
    vector,
    X is a n x k matrix, and A is a k x 1 vector. You can assume that

    any square matrices that you encounter have full rank."

    Usually this could be solved easily just by multiplying by the inverse of X, but since X is not a square matrix, I don't know what to do.

    Thanks!
    You need to manufacture a square matrix from X.

    To do this, pre-multiply both sides by the TRANSPOSE of X.

    Then you can pre-multiply both sides of the equation by the inverse of the new square matrix.


    X^TXA = X^TB

    (X^TX)^{-1}X^TXA = (X^TX)^{-1}X^TB

    IA = (X^TX)^{-1}X^TB

    A = (X^TX)^{-1}X^TB.
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  3. #3
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    Thank you so much!!! I get it now!
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