Matrices and Linear Equations Systems

  • Rafael Martínez-GuerraEmail author
  • Oscar Martínez-Fuentes
  • Juan Javier Montesinos-García
Part of the Mathematical and Analytical Techniques with Applications to Engineering book series (MATE)


In this chapter basic concepts about matrices and linear algebra is introduced, in order to present the information in a easy to understand manner, the first subject is algebraic operations with real numbers, then linear operation with real number vectors, followed by the definition of a matrix and its basic operations, next the change of basis for a matrix is given, finally Gauss Jordan method is presented.


  1. 1.
    Hoffman, K., Kunze, R.: Linear Algebra. Prentice-Hall, Englewood Cliffs (1971)Google Scholar
  2. 2.
    Axler, S.: Linear Algebra Done-Right. Springer, New York (1997)CrossRefGoogle Scholar
  3. 3.
    Grossman, S.: Elementary Linear Algebra, Wadsworth Publishing, Belmont (1987)Google Scholar
  4. 4.
    Lipschutz, S.: Linear Algebra. McGraw Hill, New York (2009)Google Scholar
  5. 5.
    Nef, W.: Linear Algebra. Dover Publications, New York (1967)Google Scholar
  6. 6.
    Lang, S.: Linear Algebra. Springer, New York (2004)Google Scholar
  7. 7.
    Anton, H.: Elementary Linear Algebra. Wiley, New York (2010)Google Scholar
  8. 8.
    Whitelaw, T.: Introduction to Linear Algebra. Chapman & Hall/CRC, Boca Raton (1992)Google Scholar
  9. 9.
    Kolman, B.: Introductory Linear Algebra an Applied First Course. Pearson Education (2008)Google Scholar
  10. 10.
    Gantmacher, F.R.: The Theory of Matrices, vol. 1. Chelsea, New York (1959)Google Scholar
  11. 11.
    Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1964)Google Scholar
  12. 12.
    Nering, E.: Linear Algebra and Matrix Theory. Wiley, New York (1970)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Rafael Martínez-Guerra
    • 1
    Email author
  • Oscar Martínez-Fuentes
    • 1
  • Juan Javier Montesinos-García
    • 1
  1. 1.Departamento de Control AutomáticoCINVESTAV-IPNMexico CityMexico

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