Eigenvalues, singular values, and Littlewood-Richardson coefficients

被引：35

作者：

Fomin, S ^{[1
]}

Fulton, W

Li, CK

Poon, YT

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI USA

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[3] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2005年 / 127卷 / 01期

关键词：

D O I：

10.1353/ajm.2005.0005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：101 / 127

页数：27

共 17 条

[1] BELKALE P, MATHAG0208107
[2] SPLITTING THE SQUARE OF A SCHUR FUNCTION INTO ITS SYMMETRICAL AND ANTISYMMETRIC PARTS
CARRE, C
LECLERC, B
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 1995, 4 (03) : 201 - 231
[3] FOMIN S, 1998, ST PETERSB MATH J, V9, P1007
[4] FOMIN S, KNUTH EQUIVALENCE TA, P413
[5] FULTOIN W, 1997, YOUNG TABLEAUX
[6] Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients
Fulton, W
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 319 (1-3) : 23 - 36
[7] Eigenvalues, invariant factors, highest weights, and Schubert calculus
Fulton, W
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 37 (03) : 209 - 249
[8] EIGENVALUES OF SUMS OF HERMITIAN MATRICES
HORN, A
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1962, 12 (01) : 225 - &
[9] Klyachko A, 1988, SELECTA MATH, V4, P419, DOI [10.1007/s000290050037, DOI 10.1007/S000290050037]
[10] Random walks on symmetric spaces and inequalities for matrix spectra
Klyachko, AA
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 319 (1-3) : 37 - 59

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