Schur-Horn theorem and Ky Fan's minimum principle for symplectic eigenvalues

TL;DR

This paper establishes the equivalence of symplectic analogues of Schur's theorem and Ky Fan's minimum principle, extending these classical results to symplectic eigenvalues and generalized means.

Contribution

It introduces symplectic versions of Schur's and Horn's theorems and proves their equivalence, extending classical inequalities to the symplectic setting.

Findings

Symplectic Schur's theorem and Ky Fan's minimum principle are equivalent.

Extended symplectic Schur's and Horn's theorems to generalized means.

Provides a unified framework for symplectic eigenvalue inequalities.

Abstract

The symplectic analogues of Schur's theorem and Ky Fan's minimum principle are shown to be equivalent. Moreover, the symplectic Schur's and Horn's theorems are extended to generalized means.