# Matrices and Linear Systems

• Tom Lyche
• Jean-Louis Merrien
Chapter
Part of the Problem Books in Mathematics book series (PBM)

## Abstract

Many complex mathematical problems have a linear system of equations hidden in it. For example, to solve a nonlinear system of equations a linearization of the problem will lead to a sequence of linear systems. To give a command to solve a general linear system $$\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}$$ in MATLAB is simple. Most often x=A∖b will do the trick. However, problems can occur. The matrix $$\boldsymbol{A}$$ can be singular or almost singular and then the computed solution can be quite inaccurate. For a better understanding of when such problems can occur one needs some background in linear algebra.

## Keywords

Linear System Cholesky Factorization Block Multiplication Positive Definite Matrice Tridiagonal Matrice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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