[Silhouette]

It's been a few years since I did serious computational linear algebra, but at that time Matrix Computations by Golub and van Loan seemed to be the standard textbook in the circles I moved in. Rather than trying to provide ready-made production-quality implementations as Numerical Recipes does, it instead concentrates on presenting the relevant mathematics, often in more depth and with more discussion than NR because it's a specialised text, with outlines of the relevant algorithms. For production use it refers to relevant BLAS/LAPACK functions so you know what to look for. If you decide to get a copy, make sure it's at least the third edition, as I think earlier editions referred to predecessor numerical libraries.

BLAS and LAPACK themselves are constantly evolving to add new or better production-quality algorithms as the field develops, and I highly recommend using the functionality they provide instead of trying to reimplement any of the basic algorithms in-house. There are heavily optimised versions of these libraries available for almost every platform you can imagine, their own documentation is pretty good, and often recent research in the field also gets written up as background papers and incorporated fairly quickly (the magic words to search for are "LAPACK working note").

If memory serves, the GSL actually depends on having a BLAS implementation available for some of its functionality, so if you're not limited by the licensing you might already be using the same sort of code under the hood anyway. :-)