59 citations · 157 across the 10 of their papers we have counts for
18 papers
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.…
Inertia of Kwong matrices
Rajendra Bhatia, Tanvi Jain
Let be any real number and for any let be distinct positive numbers. A Kwong matrix is the matrix whose entry is $(p_i^r+p_j^r)/(p_i+p_…
None Shall Pass: A blockchain-based federated identity management system
Shlok Gilda, Tanvi Jain, Aashish Dhalla
Authentication and authorization of a user's identity are generally done by the service providers or identity providers. However, these centralized systems limit the user's control…
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…
A Szegő type theorem and distribution of symplectic eigenvalues
Rajendra Bhatia, Tanvi Jain, Ritabrata Sengupta
We study the properties of stationary G-chains in terms of their generating functions. In particular, we prove an analogue of the Szegő limit theorem for symplectic eigenvalues, de…
Derivatives of symplectic eigenvalues and a Lidskii type theorem
Tanvi Jain, Hemant K. Mishra
Associated with every real positive definite matrix there exist positive numbers called the symplectic eigenvalues of and a basis of c…
Hadamard powers of rank two, doubly nonnegative matrices
Tanvi Jain
We study ranks of the Hadamard powers of doubly nonnegative matrices and show that the matrix is positive definite for every doubly nonnega…
A Schur-Horn Theorem for symplectic eigenvalues
Rajendra Bhatia, Tanvi Jain
Let and be positive -vectors. We show that there exists a positive definite real matrix whose symplectic spectrum is and the symplectic spectrum of wh…
Matrix versions of the Hellinger distance
Rajendra Bhatia, Stephane Gaubert, Tanvi Jain
On the space of positive definite matrices we consider distance functions of the form $d(A,B)=\left[\tr\mathcal{A}(A,B)-\tr\mathcal{G}(A,B)\right]^{1/2},$ where …
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…
Hadamard powers of some positive matrices
Tanvi Jain
Positivity properties of the Hadamard powers of the matrix for distinct positive real numbers and the matrix $\begin{bmatrix…
On symplectic eigenvalues of positive definite matrices
Rajendra Bhatia, Tanvi Jain
If is a real positive definite matrix, then there exists a symplectic matrix such that $M^TAM = \left [ \begin{array}{cc} D & O \\ O & D \end{array} \right ]…
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…
Inertia of Loewner Matrices
Rajendra Bhatia, Shmuel Friedland, Tanvi Jain
Given positive numbers p_1 < p_2 < ... < p_n, and a real number r let L_r be the n by n matrix with its (i,j) entry equal to (p_i^r-p_j^r)/(p_i-p_j). A well-known theorem of C. Loe…
On some positive definite functions
Rajendra Bhatia, Tanvi Jain
We study the function $(1 - \|x\|)\slash (1 - \|x\|^r),$ and its reciprocal, on the Euclidean space with respect to properties like being positive definite, conditi…
Derivatives of tensor powers and their norms
Rajendra Bhatia, Priyanka Grover, Tanvi Jain
The norm of the th derivative of the map that takes an operator to its th antisymmetric tensor power is evaluated. The case has been studied earlier by Bhatia and Fried…