Eventual positivity of tridiagonal sign patterns

Abstract

An real matrix is said to be eventually positive if there exists a positive integer such that for all . An sign pattern is said to be potentially eventually positive (PEP) if there exists some real matrices with the same sign pattern as such that is eventually positive. An sign pattern is said to be a minimal potentially eventually positive sign pattern (MPEP sign pattern) if is PEP and no proper subpattern of is potentially eventually positive. In this paper, the potential eventual positivity of tridiagonal sign patterns is investigated. All minimal potentially eventually positive tridiagonal sign patterns are identified. Consequently, all potentially eventually positive tridiagonal sign patterns are classified.