Matrices Totally Positive Relative to a Tree

Charles R. Johnson, Roberto S. Costas-Santos, and Boris Tadchiev
Arxiv ID: 0710.1366Last updated: 6/30/2020
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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