3 citations · 6 across the 15 of their papers we have counts for
15 papers
Finite-orbit obstructions for multipliers on the polydisk
Ilya Krishtal, Javad Mashreghi, Prateek Kumar Vishwakarma
We study the closed spans of finitely many joint orbits of holomorphic multipliers on the Hardy space of the polydisk. If fewer than symbols are used, every…
Hyperbolic distance matrix completion
Mihai Putinar, Prateek Kumar Vishwakarma
A completion theory for hyperbolic distance data is developed at the interface of matrix analysis, graph theory, and hyperbolic geometry. Krein's characterization of the metric spa…
Positivity preservers over finite fields II
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1
We say that a matrix over a finite field is positive definite if it is symmetric and each of its leading principal minors is a nonzero square in . In p…
Oppenheim--Schur inequalities for causal products
Dominique Guillot, Javad Mashreghi, Prateek Kumar Vishwakarma
We establish a class of Oppenheim--Schur-type inequalities for the convolutional Jury product of positive semidefinite matrices. These results extend to a causal convolutional sett…
Sharp lower bounds for generalized operator products
Dominique Guillot, Javad Mashreghi, Prateek Kumar Vishwakarma
We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and…
Functional Calculi, Positivity, and Convolution of Matrices
Javad Mashreghi, Mostafa Nasri, Prateek Kumar Vishwakarma
Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution de…
Cholesky decomposition for symmetric matrices over finite fields
Prateek Kumar Vishwakarma
Inspired by the seminal work of André-Louis Cholesky -- whose contributions remain crucial in broader sciences even after more than a century -- Cooper, Hanna and Whitlatch (2024)…
Cholesky decomposition for symmetric matrices, Riemannian geometry, and random matrices
Apoorva Khare, Prateek Kumar Vishwakarma
For each and sign pattern , we introduce a cone of real symmetric matrices : those with leading principal minors of signs $ε_k…
Entrywise transforms preserving matrix positivity and non-positivity
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1
We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definit…
Chevalley operations on TNN Grassmannians
Prateek Kumar Vishwakarma
Lusztig showed that invertible totally nonnegative (TNN) matrices form a semigroup generated by positive diagonal matrices and Chevalley generators. From its Grassmann analogue, we…
Positivity preservers over finite fields
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1
We resolve an algebraic version of Schoenberg's celebrated theorem [Duke Math.J., 1942] characterizing entrywise matrix transforms that preserve positive definiteness. Compared to…
Plücker inequalities for weakly separated coordinates in totally nonnegative Grassmannian
Daniel Soskin, Prateek Kumar Vishwakarma
We show that the partial sums of the long Plücker relations for pairs of weakly separated Plücker coordinates oscillate around on the totally nonnegative part of the Grassmanni…
Inequalities for totally nonnegative matrices: Gantmacher--Krein, Karlin, and Laplace
Shaun M. Fallat, Prateek Kumar Vishwakarma
A real linear combination of products of minors which is nonnegative over all totally nonnegative (TN) matrices is called a determinantal inequality for these matrices. It is refer…
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
Sarah Allred, Emelie Curl, Shaun Fallat +4
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently t…
Positivity preservers forbidden to operate on diagonal blocks
Prateek Kumar Vishwakarma
The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that a…