Geodesic
Matrices totally positive relative to a tree
The electronic journal of linear algebra, Tome 18 (2009), pp. 211-221.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 15A18, 94C15
Keywords: totally positive matrices, Sylvester's identity, graph theory, spectral theory 
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     title = {Matrices totally positive relative to a tree},
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Johnson, Charles R.; Costas-Santos, Roberto S.; Tadchiev, Boris. Matrices totally positive relative to a tree. The electronic journal of linear algebra, Tome 18 (2009), pp. 211-221. http://geodesic.mathdoc.fr/item/ELA_2009__18__a40/