LAPACK (Linear Algebra PACKage) - Library open source containing solvers main tasks of linear algebra . Written in Fortran using another library BLAS .
There are also counterparts, maintain or even extend the functionality and provide better performance:
Intel ® MKL 
AMD ACML ™ 
Sun Performance Library 
NAG's LAPACK 
HP's mLib 
Some implementations have support for parallel execution of functions on a multiprocessor computer systems with shared memory. Analog computer with distributed memory are libraries ScaLAPACK  and PLAPACK  .