## Matrices Totally Positive Relative to a Tree, II

Costas-Santos, R. S. and Johnson, C. R.**Linear Algebra and its Applications**505 (2016), 1 — 10

## Abstract

If *T* is a labelled tree, *A* is totally positive relative to *T* , principal submatrices of *A* associated with deletion of pendent vertices of *T* are *P*-matrices, and *A* has positive determinant, then the smallest absolute eigenvalue of *A* is positive with multiplicity 1 and its eigenvector is signed according to *T*. This conclusion has been incorrectly conjectured under weaker hypotheses.

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## BibTeX

@article {MR3506481, AUTHOR = {Costas-Santos, R. S. and Johnson, C. R.}, TITLE = {Matrices totally positive relative to a tree, {II}}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {505}, YEAR = {2016}, PAGES = {1--10}, ISSN = {0024-3795}, MRCLASS = {15B48 (05C05 05C50 15A18 94C15)}, MRNUMBER = {3506481}, ZBL = {1337.15025}, MRREVIEWER = {Carlos Marijuan}, DOI = {10.1016/j.laa.2016.04.021}, URL = {http://dx.doi.org/10.1016/j.laa.2016.04.021}, }