# Routines for Matrix Inversion

It is seldom necessary to compute an explicit inverse of a matrix. In particular, do not attempt to solve a system of equations `Ax = b` by first computing `A-1` and then forming the matrix-vector product `x = A-1b`. Call a solver routine instead (see Routines for Solving Systems of Linear Equations); this is more efficient and more accurate.

However, matrix inversion routines are provided for the rare occasions when an explicit inverse matrix is needed.

- ?getri
  Computes the inverse of an LU-factored general matrix.
- ?potri
  Computes the inverse of a symmetric (Hermitian) positive-definite matrix.
- ?pptri
  Computes the inverse of a packed symmetric (Hermitian) positive-definite matrix
- ?sytri
  Computes the inverse of a symmetric matrix.
- ?hetri
  Computes the inverse of a complex Hermitian matrix.
- ?sptri
  Computes the inverse of a symmetric matrix using packed storage.
- ?hptri
  Computes the inverse of a complex Hermitian matrix using packed storage.
- ?trtri
  Computes the inverse of a triangular matrix.
- ?tptri
  Computes the inverse of a triangular matrix using packed storage.

Parent topic: Computational Routines