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Math Help - Matrix differentiation

  1. #1
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    Matrix differentiation

    I've never done matrix differentiation before, and I want to differentiate this:

    (Y-X\theta)^{T}(Y-X\theta) with respect to \theta. I'm told that, using the product rule, we get:

    2X^{T}(Y-X\theta).

    (In the above, X, Y and \theta are all column matrices). Can someone very quickly run through this for me please? Thanks.
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  2. #2
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    Quote Originally Posted by Amanda1990 View Post
    I've never done matrix differentiation before, and I want to differentiate this:

    (Y-X\theta)^{T}(Y-X\theta) with respect to \theta. I'm told that, using the product rule, we get:

    2X^{T}(Y-X\theta).

    (In the above, X, Y and \theta are all column matrices). Can someone very quickly run through this for me please? Thanks.
    they can't be all column matrices because then X \theta wouldn't be defined. post the correct version of your problem if you still want to get help.
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  3. #3
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    Yes, sorry. What I meant to say was that Y is an n x 1 column vector, X is an n x 2 matrix and \theta is a 2 x 1 matrix.

    (Although I think the idea is the same if X is just a n x p matrix and \theta is a p x 1 matrix for a general p).
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