Paper: Matrices Totally Positive Relative to a Tree, II

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},
}