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The Eigenvalues of Complementary Principal Submatrices of a Positive Definite Matrix

Published online by Cambridge University Press:  20 November 2018

R. C. Thompson  and
S. Therianos
R. C. Thompson
Affiliation:
The University of California, Santa Barbara, California
S. Therianos
Affiliation:
The University of California, Santa Barbara, California
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Let C be an n-square Hermitian matrix, presented in partitioned form as

where A is a-square and B is b-square. Let denote the eigenvalues of C, A, B, respectively. In a recent paper [10] the following inequality was established:

1.1

if

1.2

This inequality is a simplification and a sharpening of an inequality established earlier in [6], and is a wide generalization of an inequality of Aronszajn [4].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 658 - 667
Copyright
Copyright © Canadian Mathematical Society 1972

References

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