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Paper: Matrices Totally Positive Relative to a Tree


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},
}