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- Title
EIGENVALUES, SINGULAR VALUES, AND LITTLEWOOD-RICHARDSON COEFFICIENTS.
- Authors
Fomin, Sergey; Fulton, William; Chi-Kwong Li; Yiu-Tung Poon
- 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.
- Subjects
EIGENVALUES; MATRICES (Mathematics); MATHEMATICAL inequalities; ALGEBRA; MATRIX inequalities; FOURIER analysis
- Publication
American Journal of Mathematics, 2005, Vol 127, Issue 1, p101
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2005.0005