Finite-Dimensional Vector Spaces and Matrices

  • Anthony N. Michel
  • Charles J. Herget

Abstract

In the present chapter we examine some of the properties of finite-dimensional linear spaces. We will show how elements of such spaces are represented by coordinate vectors and how linear transformations on such spaces are represented by means of matrices. We then will study some of the important properties of matrices. Also, we will investigate in some detail a special type of vector space, called the Euclidean space. This space is one of the most important spaces encountered in applied mathematics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [4.1]
    N. R. Amundson, Mathematical Methods in Chemical Engineering: Matrices and Their Applications. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1966.MATHGoogle Scholar
  2. [4.2]
    R. E. Bellman, Introduction to Matrix Algebra. New York: McGraw-Hill Book Company, Inc., 1970.Google Scholar
  3. [4.3]
    F. Brauer and J. A. Nohel, Qualitative Theory of Ordinary Differential Equations: An Introduction. New York: W. A. Benjamin, Inc., 1969.Google Scholar
  4. [4.4]
    E. T. Browne, Introduction to the Theory of Determinants and Matrices. Chapel Hill, N.C.: The University of North Carolina Press, 1958.MATHGoogle Scholar
  5. [4.5]
    E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations. New York: McGraw-Hill Book Company, Inc., 1955.MATHGoogle Scholar
  6. [4.6]
    F. R. Gantmacher, Theory of Matrices. Vols. I, II. New York: Chelsea Publishing Company, 1959.MATHGoogle Scholar
  7. [4.7]
    P. R. Halmos, Finite Dimensional Vector Spaces. Princeton, N.J.: D. Van Nostrand Company, Inc., 1958.MATHGoogle Scholar
  8. [4.8]
    K. Hoffman and R. Kunze, Linear Algebra. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1961.Google Scholar
  9. [4.9]
    S. Lipschutz, Linear Algebra. New York: McGraw-Hill Book Company, 1968.Google Scholar
  10. [4.10]
    B. Noble, Applied Linear Algebra. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1969.MATHGoogle Scholar
  11. [4.11]
    L. S. Pontriagin, Ordinary Differential Equations. Reading, Mass.: Addison-Wesley Publishing Co., Inc., 1962.Google Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Anthony N. Michel
    • 1
  • Charles J. Herget
    • 2
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Herget AssociatesAlamedaUSA

Personalised recommendations