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Eigenvalues, singular values, and Littlewood-Richardson coefficients
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 1, February 2005
- pp. 101-127
- 10.1353/ajm.2005.0005
- Article
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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.