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