The LinearAlgebraPackage (LAPACK) is an important source of good quality subroutines for NumericalAnalysis for LinearAlgebra. See http://en.wikipedia.org/wiki/LAPACK.
It uses and depends on the BasicLinearAlgebraSubprograms (BLAS) which provide low level matrix and vector operations. See http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms
There is also a version which works on distributed systems with multiple processors - ScaLapack.
The routines are in FortranLanguage and there are also interfaces to CeePlusPlus.
October 2007 For the first time in many years LAPACK development has resumed and new versions of this and ScaLapack are available from this site.
http://www.netlib.org/lapack-dev/
October 2009 See http://icl.cs.utk.edu/magma/ for MAGMA (MagmaLibrary), an extension to Lapack to make use of GeneralPurposeGraphicsProcessUnits (GPGPUs) for computation. It is in its early stages. For more about it see http://www.linux-mag.com/id/7477 -- JohnFletcher
May 2012 The BLAS implementation OpenBlas contains an uptodate implementation of LAPACK.