Matrices Totally Positive Relative to a Tree, II

Abstract

In this paper we prove that for a general tree $T$, if $A$ is T-TP, all the submatrices of $A$ associated with the deletion of pendant vertices are $P$-matrices, and $\det A>0$, then the smallest eigenvalue has an eigenvector signed according to $T$.

arXiv comment11 pages, 2 figures, submitted to LAA