1 citations · 1 across the 1 of their papers we have counts for
8 papers
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…
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 $Î…