## Matrices Totally Positive Relative to a Tree

Johnson, Charles R.; Costas-Santos, Roberto S. and Tadchiev, Boris**Electronic Journal of Linear Algebra**18 (2009), 211 — 221 INT LINEAR ALGEBRA SOC (USA) | ISSN:1537-9582 | JCR® 2009 Impact Factor: 0.892 - MATHEMATICS -- position: 64/255 (Q2/T1)

## 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.

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## BibTeX

@article {MR2505131, AUTHOR = {Johnson, Charles R. and Costas-Santos, Roberto S. and Tadchiev, Boris}, TITLE = {Matrices totally positive relative to a tree}, JOURNAL = {Electron. J. Linear Algebra}, FJOURNAL = {Electronic Journal of Linear Algebra}, VOLUME = {18}, YEAR = {2009}, PAGES = {211--221}, MRCLASS = {15B48 (05C05 05C50 15A18 94C15)}, MRNUMBER = {2505131}, ZBL = {1171.15021}, MRREVIEWER = {Carlos Mariju\'{a}n}, DOI = {10.13001/1081-3810.1306}, URL = {https://doi.org/10.13001/1081-3810.1306}, }