Regular, pseudo-regular, and almost regular matrices

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125307We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Hoffman, Wolfe, and Hoffmeister.Functional AnalysisCombinatorics15A42Regular, pseudo-regular, and almost regular matricestext