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Eigenvalues of partitioned hermitian matrices

Published online by Cambridge University Press:  17 April 2009

Robert C. Thompson  and
Linda J. Freede
Robert C. Thompson
Affiliation:
The University of California, Santa Barbara, California, USA.
Linda J. Freede
Affiliation:
The University of California, Santa Barbara, California, USA.
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Abstract

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Let C = (Aij)1≤i, j≤t be a hermitian matrix in partitioned form; here Aij, is an ni × nj. block. The purpose of this paper is to obtain inequalities linking the eigenvalues of C to those of the main diagonal blocks A11, …, Att of C.

These inequalities include, as special cases, inequalities due to N. Aronszajn and A. Hoffman.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 23 - 37
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Amir-Moéz, Ali R., “Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations”, Duke Math. J. 23 (1956), 463–476.CrossRefGoogle Scholar
[2] Fan, Ky, “Maximum properties and inequalities for the eigenvalues of completely continuous operators”, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 760–766.CrossRefGoogle ScholarPubMed
[3] Hamburger, H.L. and Grimshaw, M.E., Linear transformations in n-dimensional vector spaces. An introduction to the theory of Rilbert spaces (Cambridge University Press, Cambridge, 1951).Google Scholar
[4] Stenger, William, “An inequality -for the eigenvalues of a class of self-adjoint operators”, Bull. Amer. Math. Soc. 73 (1967), 487–490.CrossRefGoogle Scholar