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Math Help - What area of mathematics would handle matrix differentiation?

  1. #1
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    What area of mathematics would handle matrix differentiation?

    ∂/∂x( x A T + (A xT + (xT A−1 x)(xT y))

    Ts are the transposes and -1 are the inverses.

    I understand partial differentiation wrt a variable.

    I understand the matrix algebra of multiplying x by the transpose of a matrix.

    I found some matrix identities but they don't help me understand why. Just need a place to start.

    Thanks for any help.
    Last edited by orangemoose; February 20th 2010 at 04:11 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by orangemoose View Post
    ∂/∂x( x A T + (A xT + (xT A−1 x)(xT y))

    Ts are the transposes and -1 are the inverses.

    I understand partial differentiation wrt a variable.

    I understand the matrix algebra of multiplying x by the transpose of a matrix.

    I found some matrix identities by sam roweis but they don't help me understand why. Just need a place to start.

    Thanks for any help.
    Good book
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  3. #3
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    That's a good book, but...

    Right, but what I need is to find out what rules apply to that differentiation.
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  4. #4
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    So you want \partial (x A^T+ Ax^T+ (x^TA- Ix)(x^Ty))/\partial x? (You have an extra left parenthesis.)

    Is A a constant matrix or is it a function of x? In any case, as long as you are carefull not to commute a product, the usual derivative laws apply.

    Assuming that A is a constant matrix, this is
    A^T+ A+ (A- I)(x^Ty)+ (x^TA- Ix)(y)
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