Matrices Totally Positive Relative to a Tree
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1366
 Bibcode:
 2007arXiv0710.1366J
 Keywords:

 Mathematics  Combinatorics;
 05C50
 EPrint:
 10 pages, LaTeX 2e, 3 figures