# Linear Solvers Basics

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.

If the coefficients in matrix A and right-hand sides in vector b are not defined exactly but rather belong to known intervals, the system is called an interval linear system. Some basic definitions and concepts used in solving interval linear systems are described in topic Interval Linear Systems.