Common linear algebra operations are often needed for electronic structure problems. In particular, matrix diagonalization can be employed for solving the Kohn-Sham eigenproblem.
The most common routines for performing basic linear algebra operations are those defined by the BLAS, with more complicated ones provided by LAPACK. Parallel versions of a subset of these routines are provided by ScaLAPACK. Many different implementations, specifically tuned for particular systems, are available.