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Math Help - Derivatives of (e.g.) functions between matrices

  1. #1
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    Derivatives of (e.g.) functions between matrices

    Hi there all,

    I've been doing some work to try and keep myself sharp over the holidays but I've reached a point where I'm doing maths I have no notes for, and one particular topic has me completely stuffed - a few more difficult derivatives, primarily on functions between matrices.

    http://www.dpmms.cam.ac.uk/site2002/...9/08sheet4.pdf

    This is my last worksheet and although I managed to fumble my way through the first 2 parts of Q6, I haven't got a clue how to approach Qns 2, the rest of 6, all of 7, 8, and 10 - i.e. the majority of the questions! I can't find the definition of a derivative for these situations anywhere online, nor for 'continuously differentiable' in cases other than R^n.

    However much help I can get would be really really appreciated, this is the only thing I can't seem to get moving on in all my work so the more assistance I can get the better.

    Thankyou -very- much in advance!
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  2. #2
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    What you need is the definition of Fréchet derivative of a function between Banach spaces.

    Fréchet derivative - Wikipedia, the free encyclopedia
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  3. #3
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    I believe the exercises can be done without using the definition of Fréchet derivative since all the spaces involved are finite dimensional. Consider the elements of M_{n} as elements of \mathbb{R}^{n\times n} and proceed.
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