Vector and Euclidean Spaces

  • 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 vector spaces and Euclidean spaces, the first part presents definitions and concepts about vector spaces and subspaces, followed by generated subspace, linear dependence and independence, bases and dimension, quotient space, Euclidean spaces and finally the GramSchidt process is given, every section includes several proposed and solved exercises.


  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.
    Nef, W.: Linear Algebra. Dover Publications (1967)Google Scholar
  4. 4.
    Nering, E.: Linear Algebra and Matrix Theory. Wiley (1970)Google Scholar
  5. 5.
    Gantmacher, F.R.: The Theory of Matrices, vol. 1. Chelsea, New York (1959)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.
    Whitelaw, T.: Introduction to Linear Algebra, Chapman & Hall/CRC (1992)Google Scholar
  9. 9.
    Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1964)Google Scholar
  10. 10.
    Lang, S.: Linear Algebra. Springer (2004)Google Scholar
  11. 11.
    Anton, H.: Elementary Linear Algebra. Wiley (2010)Google Scholar
  12. 12.
    kolman, B.: Introductory Linear Algebra an Applied First Course. Pearson Education (2008)Google Scholar
  13. 13.
    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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