7 papers
Invertible linear preservers of semipositive matrices - a dimension free approach
Vatsalkumar N. Mer
An m-by-n real matrix A is said to be semipositive if there exists a vector x>0 such that Ax>0, where the inequalities are understood componentwise. Dorsey et al. conjectured that…
On the Wasserstein barycenter of positive definite operators
Sejong Kim, Vatsalkumar N. Mer, Miklós Pálfia
We extend the Bures-Wasserstein mean of positive definite matrices to the case of positive definite operators on a Hilbert space. This is done through its defining stationary point…
A multivariable mean equation arising from the spectral geometric mean
Sejong Kim, Vatsalkumar N. Mer
In the 1980s, Kubo and Ando introduced operator means on , the open convex cone of positive definite operators. One significant example is the weighted geometric mean $…
New multivariable mean from nonlinear matrix equation associated to the harmonic mean
Sejong Kim, Vatsalkumar N. Mer
Various multivariable means have been defined for positive definite matrices, such as the Cartan mean, Wasserstein mean, and Rényi power mean. These multivariable means have corres…
Linear preservers of copositive and completely positive matrices
Sachindranath Jayaraman, Vatsalkumar N. Mer
The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices that leaves invariant the closed…
On linear preservers of semipositive matrices
Sachindranath Jayaraman, Vatsalkumar N. Mer
Given proper cones and in and , respectively, an matrix with real entries is said to be semipositive if there exists a $x…
A characterization of nonnegativity relative to proper cones
Chandrashekaran Arumugasamy, Sachindranath Jayaraman, Vatsalkumar N. Mer
Let be an matrix with real entries. Given two proper cones and in and , respectively, we say that is nonnegative if $A…