6 papers · 1 filter
The numerical radius and positivity of block matrices
Rajendra Bhatia, Tanvi Jain
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties.…
Sums and products of symplectic eigenvalues
Tanvi Jain
For every real positive definite matrix there exists a real symplectic matrix such that $M^TAM=\diag(D,D),$ where is the positive diagonal ma…
Strong Convexity of Sandwiched Entropies and Related Optimization Problems
Rajendra Bhatia, Tanvi Jain, Yongdo Lim
We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrised version of the classical fi…
Positivity properties of the matrix
Rajendra Bhatia, Tanvi Jain
Let be positive real numbers. It is shown that the matrix whose entry is is infinitely divisible, nonsingular and totally positive.
Inequalities for the Wasserstein mean of positive definite matrices
Rajendra Bhatia, Tanvi Jain, Yongdo Lim
We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean…
On the Bures-Wasserstein distance between positive definite matrices
Rajendra Bhatia, Tanvi Jain, Yongdo Lim
The metric $d(A,B)=\left[ \tr\, A+\tr\, B-2\tr(A^{1/2}BA^{1/2})^{1/2}\right]^{1/2}$ on the manifold of positive definite matrices arises in various optimisation problem…