Eigenvalues, singular values, and Littlewood-Richardson coefficients

Details Eigenvalues, singular values, and Littlewood-Richardson coefficients Eigenvalues, singular values, and Littlewood-Richardson coefficients

2003-01-26

arxiv.org/abs/math/0301307v2

Mathematics

Algebraic Geometry

24 pages. This is the final version, to appear in American Journal of Mathematics

Scientific paper

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.

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