2 papers
math.CA2026
Negativity-preserving transforms of tuples of symmetric matrices
Alexander Belton, Dominique Guillot, Apoorva Khare +1
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obta…
math.RA2025
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…