Good source for self study of matrix decompositions What is a good source for study of various types of matrix decomposition, which is both comprehensive and also includes applications? It should at least cover LU, RQ, SVD, spectral, Schur, and eigenvalue decompositions. Extension to infinite dimensional spaces is a plus.
 A: Two books immediately come to mind:


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*Numerical Linear Algebra by Trefethen and Bau

*Matrix Computation by Gene Golub and Van Loan


The first one is fairly readable on your own and is written in a Lecture-wise format. I would hihgly recommend it if you want to get a good understanding of numerical linear algebra.
The second book is practically the bible of computational linear algebra. If you have time to read one book on numerical linear algebra, read the Matrix Computation. It is dense and fairly involved but you won't regret it. Some people complain that the book is a bit dated but I assure you, it doesn't matter. The book isn't a "numerical recipe" resource which you flip open when you need to implement something; it is much more than that. It teaches you mathematics, computation and the interplay of the two.
You can also look at Applied Numerical Linear Algebra by Demmel but personally I didn't like the book much and as compared to the other two, it is much less comprehensive.
