Off-diagonal Submatrices of a Hermitian Matrix
نویسندگان
چکیده
A necessary and sufficient condition is given to a p × q complex matrix X to be an off-diagonal block of an n × n Hermitian matrix C with prescribed eigenvalues (in terms of the eigenvalues of C and singular values of X). 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 S of all such matrices are derived from the main result. These results improve earlier ones that only give partial information for the set S.
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