Tanvi Jain

activity

20172021

collaborators

10 papers

math.FA2021

Sums and products of symplectic eigenvalues

Tanvi Jain

For every $2 n \times 2 n$ real positive definite matrix $A,$ there exists a real symplectic matrix $M$ such that $M^TAM=\diag(D,D),$ where $D$ is the $n \times n$ positive diagonal ma…

math.CA2020

Hadamard powers of rank two, doubly nonnegative matrices

Tanvi Jain

We study ranks of the $r th$ Hadamard powers of doubly nonnegative matrices and show that the matrix $A^{\circ r}$ is positive definite for every $n \times n$ doubly nonnega…

math.CA2020

A Schur-Horn Theorem for symplectic eigenvalues

Rajendra Bhatia, Tanvi Jain

Let $x$ and $y$ be positive $n$ -vectors. We show that there exists a $2 n \times 2 n$ positive definite real matrix whose symplectic spectrum is $y,$ and the symplectic spectrum of wh…

math-ph2019

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 $A (A, B)$ …

math.FA2018

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…

math.CA2018

Hadamard powers of some positive matrices

Tanvi Jain

Positivity properties of the Hadamard powers of the matrix $[1 + x_{i} x_{j}]$ for distinct positive real numbers $x_{1}, \dots, x_{n}$ and the matrix $\begin{bmatrix…