Derivatives of symplectic eigenvalues and a Lidskii type theorem

Authors

Tanvi Jain, Indian Statistical Institute (Delhi Centre)
Hemant Kumar Mishra, Indian Statistical Institute (Delhi Centre)

Article Type

Research Article

Publication Title

Canadian Journal of Mathematics

Abstract

Associated with every 2n × 2n real positive definite matrix A, there exist n positive numbers called the symplectic eigenvalues of A, and a basis of R2n called the symplectic eigenbasis of A corresponding to these numbers. In this paper, we discuss differentiability and analyticity of the symplectic eigenvalues and corresponding symplectic eigenbasis and compute their derivatives. We then derive an analogue of Lidskii’s theorem for symplectic eigenvalues as an application .

First Page

457

Last Page

485

DOI

10.4153/S0008414X2000084X

Publication Date

4-2-2022

Comments

Open Access, Green

Recommended Citation

Jain, Tanvi and Mishra, Hemant Kumar, "Derivatives of symplectic eigenvalues and a Lidskii type theorem" (2022). Journal Articles. 3165.
https://digitalcommons.isical.ac.in/journal-articles/3165