Pseudo skew-symmetric matrices over max-plus algebras

Abstract

In this paper, we consider some properties of symmetric and skew-symmetric matrices over max-plus algebras. These classes of matrices have certain features that are valid in conventional linear algebras but not in max-plus algebras, and vice versa. Taking this into account, we can describe a new class of matrices over a max-plus algebra - a class of pseudo skew-symmetric matrices. Pseudo skew-symmetric
matrices are square matrices with a zero diagonal whose symmetric elements cannot be negative at the same time. The basic properties of this class of matrices will be introduced and proved in this study.