3 citations · 6 across the 15 of their papers we have counts for
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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…