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arXiv · 2004.11024

Derivatives of symplectic eigenvalues and a Lidskii type theorem

Tanvi Jain·Hemant K. Mishra
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Abstract

Associated with every $2n\times 2n$ real positive definite matrix $A,$ there exist $n$ positive numbers called the symplectic eigenvalues of $A,$ and a basis of $\mathbb{R}^{2n}$ called the symplectic eigenbasis of $A$ corresponding to these numbers. In this paper, we discuss the differentiability (analyticity) of the symplectic eigenvalues and corresponding symplectic eigenbasis for differentiable (analytic) map $t\mapsto A(t),$ and compute their derivatives. We then derive an analogue of Lidskii's theorem for symplectic eigenvalues as an application.

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BibTeXRIS

Tanvi Jain, Hemant K. Mishra. 2020-04-23. Derivatives of symplectic eigenvalues and a Lidskii type theorem. https://doi.org/10.4153/s0008414x2000084x

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