Variational principles for symplectic eigenvalues

Authors

Rajendra Bhatia, Ashoka University
Tanvi Jain, Indian Statistical Institute (Delhi Centre)

Article Type

Research Article

Publication Title

Canadian Mathematical Bulletin

Abstract

If A is a real 2n × 2n positive definite matrix, then there exists a symplectic matrix M such that MTAM = diag(D, D), where D is a positive diagonal matrix with diagonal entries d1(A) ≤ ··· ≤ dn(A). We prove a maxmin principle for dk (A) akin to the classical Courant-Fisher-Weyl principle for Hermitian eigenvalues and use it to derive an analogue of the Weyl inequality di+j-1(A + B) ≥ di(A) + dj(B).

First Page

553

Last Page

559

DOI

10.4153/S0008439520000648

Publication Date

8-20-2020

Recommended Citation

Bhatia, Rajendra and Jain, Tanvi, "Variational principles for symplectic eigenvalues" (2020). Journal Articles. 171.
https://digitalcommons.isical.ac.in/journal-articles/171