Proceedings of the American Mathematical Society

Author(s): Chi-Kwong Li; Yiu-Tung Poon
Journal: Proc. Amer. Math. Soc. 132 (2004), 2849-2856.
MSC (2000): Primary 15A18, 15A42
Posted: June 2, 2004
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Abstract: A necessary and sufficient condition is given to a $p\times q$ complex matrix

to be an off-diagonal block of an $n\times n$ 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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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

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