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Math Help - Matrix Calculus - Transpose of Vector Derivatives

  1. #1
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    Matrix Calculus - Transpose of Vector Derivatives

    Hi all,

    Here's a newbie question for you:

    What are the derivatives of the following -->

    Matrix Calculus - Transpose of Vector Derivatives-qqq.png

    I guess some of these results will be transposed and othes not..? And some will be vectors or matrices?

    Cheers,
    Daniel BS.

    ps: couldn't insert my equations within [tex] tags anyhow!
    Got a message of a 25 chars limit! Is a there a way through?
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  2. #2
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    About the tag thing, nervermind, it was the keywords tag not the math tag... anyways... main question persists.. =)
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  3. #3
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    To avoid the character limit, break your LaTex into parts.
    \frac{\partial x}{\partial x}, \frac{\partial x^T}{\partial x}, \frac{\partial x}{\partial x^T}, \frac{\partial x^T}{\partial x^T}.

    Now what definition of differentiation by a vector are you using?
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  4. #4
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    Sorry about the english mistakes,

    Well, by this equation (D-3):
    http://www.colorado.edu/engineering/.../IFEM.AppD.pdf

    if y = x, then
    \frac{\partial \mathbf{x}}{\partial \mathbf{x}}=I

    but I know that it should be 1, right? So, I differs from 1? I know they both share the similar property of being neutral elements, but they're still distinct results, right?

    Furthermore, what about the transposed ones? What are they equal of?

    Regards
    Daniel.
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  5. #5
    MHF Contributor

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    That was why I asked, before, "what definition of differentiation by a vector are you using?"- which you have still not answered. There are several different ways of defining that derivative. The most general defines the derivative of one vector by another to be a linear transfomation that best approximates the vector function. If that is the definition you are using then "I" is the identity linear transformation: I(v)= v. Another definition gives the derivative of a vector, u, by a vector, v, as the matrix having the partial derivatives of each component of vector u, with respect to vector v's components, as rows. In that case "I" is the identity matrix.

    You obviously can't do this problem unless you know which definition you are using!
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