The matrix inverse, A^{-1}, is a mathematical relationship such that given a square n x n matrix A, A*A^{-1} = A^{-1}*A = I, where I is the identity matrix. Use this tag with regards to any numerical methods or computations that require the use or calculation of the matrix inverse.
Computation of the inverse of a square matrix, provided it is invertible (i.e., full-rank), is often via LU factorization. When the matrix is positive-definite, Cholesky factorization is often used. In standard numerical linear algebra library lapack, dgesv and dpotrf respectively performs LU and Cholesky factorization.
In reality it is rare that a matrix inverse needs be explicitly formed, and matrix multiplications involving a matrix inverse is done by one of the factorizations above, and a triangular system solving.
