Paths and Cycles in the Totally Positive Completion Problem

Abstract

An n x n real matrix is said to be totally positive if every minor is nonnegative. In this paper, we are interested in totally positive completion problems, that is, when a partial totally positive matrix has a totally positive matrix completion. This problem has, in general, a negative answer when the graph of the specified entries of the partial matrix is a path or a cycle. For these cases, we obtain necessary and sufficient conditions in order to obtain the desired completion.