𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Eigenvalue Inequalities and Schubert Calculus

✍ Scribed by Uwe Helmke; Joachim Rosenthal

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
733 KB
Volume
171
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Using techniques from algebraic topology we derive linear inequalities which relate the spectrum of a set of Hermitian matrices A I, . . . , A, E C" " " with the spectrum of the sum A + . . . + A,.

These extend eigenvalue inequalities due to FREEDE-THOMPSON and HORN for sums of eigenvalues of two Hermitian matrices.

πŸ“œ SIMILAR VOLUMES

Noncommutative Schubert Calculus and Gro
Noncommutative Schubert Calculus and Grothendieck Polynomials
✍ Cristian Lenart πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 236 KB

In this paper we extend the work of Fomin and Greene on noncommutative Schur functions by defining noncommutative analogs of Schubert polynomials. If the variables satisfy certain relations (essentially the same as those needed in the theory of noncommutative Schur functions), we prove a Pieri-type

Operator Calculus forQ̃-Polynomials and
Operator Calculus forQ̃-Polynomials and Schubert Polynomials
✍ Alain Lascoux; Piotr Pragacz πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 522 KB

de die a maria Contents. ## Introduction. 1. Divided differences associated with the hyperoctahedral groups. 2. Reproducing kernels and a vanishing property. 3. Action of s on the basis [S + } Q I ] an inductive approach. 4. Action of s on the basis [S + } Q I ] via the vanishing property. ## 5

Eigenvalue inequalities and equalities
Eigenvalue inequalities and equalities
✍ Roger A. Horn; Noah H. Rhee; So Wasin πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 610 KB

We consider cases of equality in three basic inequalities for eigenvalues of Hermitian matrices: Cauchy's interlacing inequalities for principal submatrices, Weyl's inequalities for sums, and the residual theorem. Several applications generalize and sharpen known results for eigenvalues of irreducib