Eigenvalues and Positive Definite Matrices

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


Eigenvalues and eigenvectors are defined. The Spectral Theorem for symmetric matrices is proved. Positive definite matrices are introduced. Idempotent matrices are defined and it is shown that for such matrices the rank equals the trace. Schur complement is defined and its application to proving characterizations of positive definite matrices is shown.

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

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

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