Using Maple to Make Manageable Matrices

  • Ana C. Camargos Couto
  • David J. JeffreyEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)


This paper describes an application of Maple in the teaching of linear algebra. The topic is the construction of an orthogonal basis for a set of vectors or a matrix using Householder transformations. We present a method for generating matrices which, when subject to using Householder transformations, require only rational computations and give rational results. The pedagogical problem addressed is that numerical examples in this topic will usually contain unsimplified square roots, which add an extra layer of difficulty for students working examples.


  1. 1.
    Cayley, A.: Sur quelques proprié tes des determinantes gauches. J. Reine Angew. Math. 32, 119–123 (1846). Reprinted in the Collected Mathematical Papers of Cayley, Cambridge University Press 1889–1898, vol. 1, pp. 332–336 MathSciNetGoogle Scholar
  2. 2.
    Corless, R.M., Fillion, N.: A Graduate Introduction to Numerical Methods. From the Viewpoint of Backward Error Analysis. Springer, New York (2013). Scholar
  3. 3.
    Demmel, J.W.: Applied Numerical Linear Algebra. SIAM press, Philadelphia (1997)CrossRefGoogle Scholar
  4. 4.
    Frisch, S., Vaserstein, L.: Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples. J. Pure Appl. Algebra 216, 184–191 (2012). Scholar
  5. 5.
    Gilbert, R.C.: Companion matrices with integer entries and integer eigenvalues and eigenvectors. Am. Math. Mon. 95(10), 947–950 (1988)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Khattak, N., Jeffrey, D.J.: Rational Orthonormal Matrices. In: 2017 IEEE SYNASC, p. 71 (2017). CPS, ISBN-13: 978-1-5386-2626-9Google Scholar
  7. 7.
    Renaud, J.-C.: Matrices with integer entries and integer eigenvalues. Am. Math. Mon. 90, 202–203 (1983)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Applied Mathematics and ORCCAThe University of Western OntarioLondonCanada

Personalised recommendations