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We establish a trace inequality of symplectic matrices via a more general trace minimization theorem. As a consequence, we derive another proof of a result in [R. Bhatia, T. Jain, On symplectic eigenvalues of positive-definite matrices, J. Math. Phys., 56 (2015),112201.]. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new version of a Schur–Horn type theorem. Meanwhile, we provide a new proof of a recent result in [Bhatia R, Jain T. A Schur-Horn theorem for symplectic eigenvalues. Linear Algebra Appl. 2020;599:133–139]. [ABSTRACT FROM AUTHOR]

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number, positive semi-definite matrices,, and generalized matrix functionssuch as the determinant and permanent, etc., we have A general scheme is introduced to prove more general inequalities involvingmpositive semi-definite matrices forthat extend the results of other authors. [ABSTRACT FROM PUBLISHER]

The main purpose of this work is to present a better bound than the recent result given by Zhang [Linear Multilinear Algebra. 2015;63:2511–2517]. [ABSTRACT FROM AUTHOR]