A Schur-Horn theorem for symplectic eigenvalues
Linear Algebra and Its Applications
Let x and y be positive n-vectors. We show that there exists a 2n×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.
Bhatia, Rajendra and Jain, Tanvi, "A Schur-Horn theorem for symplectic eigenvalues" (2020). Journal Articles. 172.