Linear Transformations

  • 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)


This chapter is about linear transformations, it begins with an elementary introduction, followed by kernel and image concepts, then linear operators and finally associate matrix.


  1. 1.
    Hoffman, K., Kunze, R.: Linear Algebra. Prentice-Hall (1971)Google Scholar
  2. 2.
    Grossman, S.: Elementary Linear Algebra. Wadsworth Publishing (1987)Google Scholar
  3. 3.
    Whitelaw, T.: Introduction to Linear Algebra. Chapman & Hall/CRC (1992)Google Scholar
  4. 4.
    Anton, H.: Elementary Linear Algebra. Wiley (2010)Google Scholar
  5. 5.
    Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1964)Google Scholar
  6. 6.
    Axler, S.: Linear Algebra Done-Right. Springer (1997)Google Scholar
  7. 7.
    Lipschutz, S.: Linear Algebra. McGraw Hill (2009)Google Scholar
  8. 8.
    Nef, W.: Linear Algebra. Dover Publications (1967)Google Scholar
  9. 9.
    Lang, S.: Linear Algebra. Springer (2004)Google Scholar
  10. 10.
    Nering, E.: Linear Algebra and Matrix Theory. Wiley (1970)Google Scholar
  11. 11.
    kolman, B.: Introductory Linear Algebra an Applied First Course. Pearson Education (2008)Google Scholar
  12. 12.
    Gantmacher, F.R.: The Theory of Matrices, vol. 1. Chelsea, New York (1959)Google Scholar
  13. 13.
    Kailath, T.: Linear Systems. Prentice-Hall, Englewood Cliffs, NJ (1980)Google Scholar
  14. 14.
    Hermann, R., Krener, A.: Nonlinear controllability and observability. IEEE Trans. Autom. Control 22(5), 728–740 (1977)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Aguilar-Lpez, R., Mata-Machuca, J.L., Martnez-Guerra, R.: Observability and Observers for Nonlinear Dynamical Systems: Nonlinear Systems Analysis. Lambert Academic Publishing (2011)Google Scholar
  16. 16.
    Halmos, P. R.: Finite-Dimensional Vector Spaces. Courier Dover Publications (2017)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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