Offdiagonal submatrices of a Hermitian matrix
Authors:
ChiKwong Li and YiuTung Poon
Journal:
Proc. Amer. Math. Soc. 132 (2004), 28492856
MSC (2000):
Primary 15A18, 15A42
Published electronically:
June 2, 2004
MathSciNet review:
2063102
Fulltext PDF Free Access
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Abstract: A necessary and sufficient condition is given to a complex matrix to be an offdiagonal 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
ChiKwong Li
Affiliation:
Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 231878795
Email:
ckli@math.wm.edu
YiuTung Poon
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email:
ytpoon@iastate.edu
DOI:
http://dx.doi.org/10.1090/S0002993904070728
PII:
S 00029939(04)070728
Keywords:
Hermitian matrices,
singular values,
eigenvalues,
LittlewoodRichardson 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
