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- W3100659610 abstract "If $A$ is a $2n times 2n$ real positive definite matrix, then there exists a symplectic matrix $M$ such that $M^TAM = left [ begin{array}{cc} D & O O & D end{array} right ]$ where $D= diag (d_1 (A), ldots, d_n(A))$ is a diagonal matrix with positive diagonal entries, which are called the symplectic eigenvalues of $A.$ In this paper we derive several fundamental inequalities about these numbers. Among them are relations between the symplectic eigenvalues of $A$ and those of $A^t,$ between the symplectic eigenvalues of $m$ matrices $A_1, ldots, A_m$ and of their Riemannian mean, a perturbation theorem, some variational principles, and some inequalities between the symplectic and ordinary eigenvalues." @default.
- W3100659610 created "2020-11-23" @default.
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- W3100659610 date "2015-11-01" @default.
- W3100659610 modified "2023-10-16" @default.
- W3100659610 title "On symplectic eigenvalues of positive definite matrices" @default.
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- W3100659610 doi "https://doi.org/10.1063/1.4935852" @default.
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