I'm a grad student trying to absorb from the book Pattern Recognition and Machine Learning. However, I found that I really need a good grasp of matrix calculus before I can deduct the formulas myself (since I think in this way learning could be more effective). For example, when deducting Gaussian Mixture Model using EM algorithm, I can't really do the M-step on my own since I don't know how to do calculus on vectors/matrix.
What I wish to solve is to be able to solve derivatives like $x^TAx$ with respect to $x$.
I did read wikipedia and know the basics of the idea of taking derivatives with respect to vector, but I hope to get a sense and make myself more confirmable with these operations.
1) Does people memorize the derivatives of the basic formulas (like $x^TAx$, or derivaitive of covariance) and then expand?
2) What good resources especially books with practices problems could be recommended?
Thanks a lot