Eigenpairs and Similarity Transformations

  • Tom Lyche
Part of the Texts in Computational Science and Engineering book series (TCSE, volume 22)


We have seen that a Hermitian matrix is positive definite if and only if it has positive eigenvalues. Eigenvalues and some related quantities called singular values occur in many branches of applied mathematics and are also needed for a deeper study of linear systems and least squares problems.


  1. 8.
    M.W. Hirsch, S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, San Diego, 1974)zbMATHGoogle Scholar
  2. 9.
    R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, UK, 1991)CrossRefGoogle Scholar
  3. 10.
    R.A. Horn, C.R. Johnson, Matrix Analysis, Second edition (Cambridge University Press, Cambridge, UK, 2013)Google Scholar
  4. 16.
    G.W. Stewart, Introduction to Matrix Computations (Academic press, New York, 1973)zbMATHGoogle Scholar
  5. 19.
    G.W. Stewart, J. Sun, Matrix Perturbation Theory (Academic Press, San Diego, 1990)zbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Tom Lyche
    • 1
  1. 1.Blindern, University of OsloOsloNorway

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