Chapter 6. Eigenvalues, Eigenvectors, and Singular Values

  1. George A. F. Seber

Published Online: 8 JUN 2007

DOI: 10.1002/9780470226797.ch6

A Matrix Handbook for Statisticians

A Matrix Handbook for Statisticians

How to Cite

Seber, G. A. F. (2007) Eigenvalues, Eigenvectors, and Singular Values, in A Matrix Handbook for Statisticians, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470226797.ch6

Author Information

  1. Department of Statistics University of Auckland, Auckland, New Zealand

Publication History

  1. Published Online: 8 JUN 2007
  2. Published Print: 7 NOV 2007

ISBN Information

Print ISBN: 9780471748694

Online ISBN: 9780470226797



  • eigenvalues;
  • eigenvectors;
  • singular values;
  • polynomials;
  • Cayley-Hamilton theorem


This chapter contains sections titled:

  • Introduction and Definitions

  • Variational Characteristics for Hermitian Matrices

  • Separation Theorems

  • Inequalities for Matrix Sums

  • Inequalities for Matrix Differences

  • Inequalities for Matrix Products

  • Antieigenvalues and Antieigenvectors