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I am a little bit struggling with matrix differentiation and I am looking to practice with as many exercises as possible, spanning from simple ones, e.g. what is the $$gradient \ of \ x^T A x$$ to more advanced exercises also involving for instance determinants or traces.

Does anyone know where could I find such a set of exercises please?

Ile
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  • On that specific gradient, there have been dozens of questions asked. Some answers are good and edifying. – Rodrigo de Azevedo Oct 30 '19 at 18:34
  • Hi - if you read my question, I am not asking for a solution to the gradient of the quadratic form (which I know). I am asking for where I can find a set of exercises covering problems that go from easy ones (e.g. of the level of what is the gradient of the quadratic form), to more complex ones (e.g. with traces,...). Thanks – Ile Oct 30 '19 at 19:05
  • Can you please provide the link of the exercises I am looking for? I have not found anything like that here on Math SE. Also, I am not looking for specific answers (which I would just google otherwise), I am looking for a complete list of exercises. – Ile Oct 30 '19 at 19:21
  • Take a look at the white wolfie's answers. He knows the material. – Rodrigo de Azevedo Oct 30 '19 at 19:26
  • The bag of tricks is not that big. Suppose you have a function $f$ that takes a matrix and produces a scalar. You would like to compute $\nabla f$. If you compute the directional derivative and find a way of writing it as an inner product, then you can extract the gradient by visual inspection. Terry Tao wrote a blog post containing several tricks. – Rodrigo de Azevedo Oct 30 '19 at 19:32

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