The Wolfram Language incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling exact, symbolic, and arbitrary-precision as well as machine-precision computation.

LinearSolve — solve a linear system, dense or sparse

LinearSolveFunction — a function created to repeatedly solve a linear system

Inverse — explicit dense matrix inverse

DrazinInverse — Drazin generalized matrix inverse

NullSpace — vectors spanning the null space of a matrix

MatrixRank — rank of a matrix

Det — determinant

Adjugate — adjugate

Minors — matrices of minors

RowReduce — generate a row echelon form

LUDecomposition  ▪  CholeskyDecomposition

UpperTriangularize  ▪  LowerTriangularize

Minimization Problems »

LeastSquares  ▪  PseudoInverse  ▪  Norm  ▪  ...