Matrices and Linear Systems

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


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.


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Tom Lyche
    • 1
  • Jean-Louis Merrien
    • 2
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.INSA de Rennes CS 70839Rennes Cedex 07France

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