Reference for matrix calculus Could someone provide a good reference for learning matrix calculus? I've recently moved to a more engineering-oriented field where it's commonly used and don't have much experience with it.
 A: Actually the books cited above by Sivaram are excellent for numerical stuff. If you want "matrix calculus" then the following books might be helpful:


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*Matrix Differential Calculus with Applications in Statistics and Econometrics by Magnus and Neudecker

*Functions of Matrices by N. Higham

*Calculus on Manifolds by Spivak
Some classic, but very useful material can also be found in


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*Introduction to Matrix Analysis by Bellman.


As a simple example, the books will teach (unless you already know it) how to compute, say, the derivative of $f(X) = \log\det(X)$ for an invertible matrix $X$.
A: Gene Howard Golub, Charles F. Van Loan book on "Matrix Computations" is regarded as the "Bhagavad Gita" for Matrix Algorithms.
http://books.google.com/books?id=mlOa7wPX6OYC&printsec=frontcover
There is also another book by "Gene Howard Golub, Gerard Meurant" on "Matrices, moments, and quadrature with applications".
http://books.google.com/books?id=IZvkFET3LlwC&printsec=frontcover
Also, "Numerical Linear Algebra" by Trefethen and Bau is well-written and easy to read.
http://books.google.com/books?id=bj-Lu6zjWbEC&printsec=frontcover
I would highly recommend Trefethen and Bau since I have read it completely. I feel it is ideal for self-study or for a one quarter course. Once you are done with this you can take a look at Golubs' book. Golubs' book is really good for reference.
