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Inequalities for Eigenvalues and Singular Values

  • R. B. Bapat
Part of the Universitext book series (UTX)

Abstract

Extremal representations for the maximum and minimum eigenvalues of a symmetric matrix are proved. Singular values are defined and the Singular Value Decomposition is obtained. Courant–Fischer Minimax Theorem, Cauchy Interlacing Principle and majorization of diagonal elements by eigenvalues of a symmetric matrix are proved. The volume of a matrix is defined as the positive square root of the product of the nonzero singular values. Some basic properties of volume are proved. Minimality properties of the Moore–Penrose inverse involving singular values are established.

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • R. B. Bapat
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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