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arXiv · 2004.03906

A Schur-Horn Theorem for symplectic eigenvalues

Rajendra Bhatia·Tanvi Jain
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Abstract

Let $x$ and $y$ be positive $n$-vectors. We show that there exists a $2n\times 2n$ positive definite real matrix whose symplectic spectrum is $y,$ and the symplectic spectrum of whose diagonal is $x$ if and only if $x$ is weakly supermajorised by $y.$

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Rajendra Bhatia, Tanvi Jain. 2020-04-08. A Schur-Horn Theorem for symplectic eigenvalues. https://arxiv.org/abs/2004.03906

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