Matrices Totally Positive Relative to a General Tree

Details Matrices Totally Positive Relative to a General Tree Matrices Totally Positive Relative to a General Tree

2010-03-25

arxiv.org/abs/1003.5160v1

Mathematics

Combinatorics

6 pages, submitted to ELA

Scientific paper

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 $T$.

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