Eigenvalues, singular values, and Littlewood-Richardson coefficients
Algebraic Geometry
2007-05-23 v2 Rings and Algebras
Abstract
We characterize the relationship between the singular values of a complex Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of an 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.
Cite
@article{arxiv.math/0301307,
title = {Eigenvalues, singular values, and Littlewood-Richardson coefficients},
author = {Sergey Fomin and William Fulton and Chi-Kwong Li and Yiu-Tung Poon},
journal= {arXiv preprint arXiv:math/0301307},
year = {2007}
}
Comments
24 pages. This is the final version, to appear in American Journal of Mathematics