Matrices Totally Positive Relative to a Tree

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

2007-10-06

arxiv.org/abs/0710.1366v4

ELA volume 18 (2009), pages 211-221

Mathematics

Combinatorics

10 pages, LaTeX 2e, 3 figures

Scientific paper

It is known that for a totally positive (TP) matrix, the eigenvalues are
positive and distinct and the eigenvector associated with the smallest
eigenvalue is totally nonzero and has an alternating sign pattern. Here, a
certain weakening of the TP hypothesis is shown to yield a similar conclusion.

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