Characterizations of {1, 3}-Bohemian inverses of structured matrices

Abstract

This paper presents {1, 3}-Bohemian inverses of a certain type of structured {?1, 0, 1}-matrices, particularly full and well-settled matrices. It begins by characterizing the rank-one Bohemian matrices for the population P = {?1, 0, 1}. Characterizations of the {3} and {1, 3}-Bohemian inverses are presented for arbitrary population over the set {?1, 0, 1}. Furthermore, explicit formulas are provided to enumerate the {1, 3}-Bohemian inverses of these matrices when the population is exactly {?1, 0, 1}. Moreover, corresponding results for {3}-inverses are obtained. © 2025, University of Nis. All rights reserved.