2024/10/26 by Erik Christensen, Christensen, Erik
Computer Science · Engineering · #15A23 #46L07 (Secondary) #52A21 #81P47 (Primary) 15A60 #Antenna Design and Optimization #Cellular Automata and Applications #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2410.20112
openalex publication_date 2024/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For positive n x n matrices with unit diagonal, we give a characterization of the extremal elements, and show that such a matrix satisfies rank(X) =< n^(1/2).