Matrices Totally Positive Relative to a Tree
Johnson, Charles R.; Costas-Santos, R. S. and Tadchiev, B. Electronic Journal of Linear Algebra 18 (2009), 211 — 221Abstract
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, C. R. and Costas-Santos, R. S. and Tadchiev, B.}, 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}, }