LAPACK (Linear Algebra Package) is a library of routines that provides fast, robust algorithms for numerical linear algebra and matrix computations. Linear algebra functions and matrix operations in MATLAB® are built on LAPACK, and they continue to benefit from the performance and accuracy of its routines.
MATLAB started its life in the late 1970s as an interactive calculator built on top of LINPACK and EISPACK, which were the state-of-the-art Fortran subroutine libraries for matrix computation of the time. For many years MATLAB used translations to C of about a dozen Fortran subroutines from LINPACK and EISPACK.
In the year 2000, MATLAB migrated to using LAPACK, which is the modern replacement for LINPACK and EISPACK. It is a large, multi-author, Fortran library for numerical linear algebra. LAPACK was originally intended for use on supercomputers because of its ability to operate on several columns of a matrix at a time. The speed of LAPACK routines is closely connected to the speed of the Basic Linear Algebra Subroutines (BLAS). The BLAS version is typically hardware-specific and highly optimized.