Tanvi Jain

On symplectic eigenvalues of positive definite matrices

If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(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 At, between the symplectic eigenvalues of m matrices A1, …, Am and of their Riemannian mean, a perturbation theorem, some variational principles, and some inequalities between the symplectic and ordinary eigenvalues.

DERIVATIVES OF TENSOR POWERS AND THEIR NORMS

The norm of the

Topological properties of the multifunction space L(X) of cusco maps

m

Mean matrices and conditional negativity

th derivative of the map that takes an operator to its

Atsuji completions vis-à-vis hyperspaces

k

Boundedly UC spaces: characterisations and preservation

th antisymmetric tensor power is evaluated. The case

Higher order derivatives and perturbation bounds for determinants

m=1

Atsuji completions: Equivalent characterisations

has been studied earlier by Bhatia and Friedland [R. Bhatia and S. Friedland, Variation of Grassman powers and spectra, Linear Algebra and its Applications, 40:1--18, 1981]. For this purpose a multilinear version of a theorem of Russo and Dye is proved: it is shown that a positive

Derivatives for antisymmetric tensor powers and perturbation bounds

m

On the Bures–Wasserstein distance between positive definite matrices

-linear map between