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Inequalities connecting the eigenvalues of a hermitian matrix with the eigenvalues of complementary principal submatrices

Published online by Cambridge University Press:  17 April 2009

Robert C. Thompson  and
S. Therianos
Robert C. Thompson
Affiliation:
University of California, Santa Barbara, California, USA.
S. Therianos
Affiliation:
University of California, Santa Barbara, California, USA.
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Abstract

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Let be a hermitian matrix in partitioned form. Let the eigenvalues of A, B, C be α1 ≥ … ≥ αa, β1 ≥ … ≥ βb, γ1 ≥ … ≥ γn, respectively. In this paper four classes of inequalities are proved comparing the αi. and βj with the γk. The simplest of these is: if the subscripts is, js satisfy 1 ≤ i1 < … < im ≤ α, 1 ≤ j1 < … < jm ≤ b.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 117 - 132
Copyright
Copyright © Australian Mathematical Society 1972

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