LAPACK

Lapack is 'THE' package for linear algebra applications. At any time you need to solve some non trivial numerical problems involving matrices, you definitely SHOULD have a look at Lapack.
I use it for matrix inversion an manipulation as well as for calculating eigenvalues and eigenvectors of very large non sparse systems and it is just wonderful to use. It can be used along with C or C++ code, despite it is written in Fortran, so once again it deserves to be studied with a lot of respect.

So, all you guys, thanks, thanks, THANKS for all the effort you are putting in this wonderful software.