Potentially nilpotent sign pattern matrices Original Research Article

A sign pattern is said to be potentially nilpotent if it allows nilpotence. In this paper, a number of qualitative necessary or sufficient conditions for a sign pattern to allow nilpotence are established. The sign patterns that allow nilpotence of index 2 are investigated. For orders up to three, potentially nilpotent sign patterns are characterized. Potentially nilpotent tree sign patterns are also explored.