Many applications in science and engineering require the solution of a system of linear equations. This problem is usually expressed mathematically by the matrix-vector equation,
Ax = b, where A is an
m-by-n matrix, x is the n element column vector and b is the m element column vector. The matrix A is usually referred to as the coefficient matrix, and the vectors x and b are referred to as the solution vector and the right-hand side, respectively.
Basic concepts related to solving linear systems with sparse matrices are described in topic Sparse Linear Systems that follows.