TITLE: Book on matrix computation
QUESTION [6 upvotes]: I'm taking a machine learning course and it involves a lot of matrix computation like compute the derivatives of a matrix with respect to a vector term. In my linear algebra course these material is not covered and I browsed some book in the school library but didn't find something relevant to my problem.
So can you recommend me a book which covers these matrix computations? 
Thanks!

REPLY [2 votes]: Bishop's excellent machine learning textbook, Pattern Recognition and Machine Learning, has an appendix on "Properties of Matrices".  One section in this appendix (p. 697) is about Matrix Derivatives, and discusses formulas like this:
\begin{equation}
\frac{\partial}{\partial A} \text{Tr}(AB) = B^T
\end{equation}
and 
\begin{equation}
\frac{\partial}{\partial A} \ln | A | = \left(A^{-1} \right)^T,
\end{equation}
for example.
Peter Lax has a great book called Linear Algebra and its Applications.  Chapter 9 is entitled "Calculus of Vector- and Matrix-Valued Functions".