On the Submultiplicativity of Matrix Norms Induced by Random Vectors

2024/02/13 by Ludovick Bouthat, Bouthat, Ludovick
Computer Science · #15A18 #15A60 #47A30 #Advanced Algebra and Logic #FOS: Mathematics #Metric Geometry (math.MG) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2402.08173

openalex publication_date 2024/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent article, Chávez, Garcia and Hurley introduced a new family of norms ‖⋅‖_X,d on the space of n × n complex matrices which are induced by random vectors X having finite d-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of X are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of X have finite p-moments for p=max\2+ε,d\.

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