Abstract

We characterize the relationship between the singular values of a Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of a Hermitian (or real symmetric) matrix C = A + B in terms of the combined list of eigenvalues of A and B. The answers are given by Horn-type linear inequalities. The proofs depend on a new inequality among Littlewood-Richardson coefficients.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 101-127
Launched on MUSE
2005-02-02
Open Access
No
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