Linear algebra is at the core of many mathematical concepts. In addition to high level functions such as Dot, Transpose, and Outer, the Wolfram Language provides, both direct access to and extensions of much of the Basic Linear Algebra Subroutines (BLAS) library. For some applications, these can provide a performance boost.

BLAS 1

ASUM — compute the sum of absolute values of vector elements

AXPY — add a vector to a scalar multiple of another vector

COPY — copy a vector to another vector

DOT — dot product of two vectors

DOTC — conjugate dot product of two vectors

IAMAX — position of the vector element with the maximum absolute value

NRM2 — compute the Euclidean norm of a vector

ROT — apply a Givens rotation to a pair of vectors

ROTG — compute the parameters for a Givens rotation

SCAL — multiply a vector by a scalar

SWAP — swap two vectors

BLAS 2

GEMV — add a vector to the product of a matrix and another vector

GER — rank-one update of a matrix

GERC — rank-one update of a complex-valued matrix

SYMV — add a vector to the product of a symmetric matrix and another vector

SYR — symmetric rank-one update of a matrix

TRMV — add a vector to the product of a triangular matrix and another vector

TRSV — solve a triangular system of linear equations

TBSV — solve a triangular system of linear equations using a banded representation

BLAS 3

GEMM — add a matrix to the product of two other matrices

HERK — Hermitian rank-k update of a matrix

SYRK — symmetric rank-k update of a matrix

TRMM — computes the product of a triangular matrix and another matrix

TRSM — solve triangular systems of linear equations