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.