Off-diagonal submatrices of a Hermitian matrix

Authors:
Chi-Kwong Li and Yiu-Tung Poon

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2849-2856

MSC (2000):
Primary 15A18, 15A42

DOI:
https://doi.org/10.1090/S0002-9939-04-07072-8

Published electronically:
June 2, 2004

MathSciNet review:
2063102

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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition is given to a complex matrix to be an off-diagonal block of an Hermitian matrix with prescribed eigenvalues (in terms of the eigenvalues of and singular values of ). The proof depends on some recent breakthroughs in the study of spectral inequalities on the sum of Hermitian matrices by Klyachko and Fulton. Some interesting geometrical properties of the set of all such matrices are derived from the main result. These results improve earlier ones that only give partial information for the set .

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Additional Information

**Chi-Kwong Li**

Affiliation:
Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795

Email:
ckli@math.wm.edu

**Yiu-Tung Poon**

Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011

Email:
ytpoon@iastate.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07072-8

Keywords:
Hermitian matrices,
singular values,
eigenvalues,
Littlewood-Richardson rules

Received by editor(s):
February 18, 2002

Received by editor(s) in revised form:
October 24, 2002

Published electronically:
June 2, 2004

Additional Notes:
The first author’s research was partially supported by an NSF grant

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society