Thread: Derivatives of (e.g.) functions between matrices

1. 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.

3. 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.