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Math Help - FOILING the difference of two matrices and its transpose, and then derivative

  1. #1
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    FOILING the difference of two matrices and its transpose, and then derivative

    Go to this page:
    https://files.nyu.edu/mrg217/public/ols_matrix.pdf/

    On p.2 there are three RHS-expressions of equation 4. How do you go from the first expression to the second expression? Matrices are not like variables x and y, that you can apply FOIL, right?

    Furthermore, how can you take the derivative of the result with respect to beta if the matrix beta has more than 1 constituent beta.

    Thanks,
    Litic
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  2. #2
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    Re: FOILING the difference of two matrices and its transpose, and then derivative

    yes, you can "FOIL" matrices:

    (A+B)(C+D) = AC + BD + AD + BC, but remember the order of multiplication in each term is important:

    (A+B)(A-B) = A2 + BA - AB - B2, NOT A2 - B2 (because usually AB ≠ BA).

    matrix differentiation is just a convenient way of keeping track of the various partial derivatives involved. you might want to look here:

    Matrix calculus - Wikipedia, the free encyclopedia
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