Minimum (maximum) rank of sign pattern tensors and sign nonsingular tensors

Abstract

In this paper, we define the sign pattern tenors, minimum (maximum) rank of sign pattern tenors, term rank of tensors and sign nonsingular tensors. The necessity and sufficiency for the minimum rank of sign pattern tenors to be 1 is given. We show that the maximum rank of a sign pattern tensor is not less than the term rank and the minimum rank of the sign pattern of a sign nonsingular tensor is not less than its dimension. We get some characterizations of tensors having sign left or sign right inverses.