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Matrices totally positive relative to a tree, II

Authors

COSTAS SANTOS, ROBERTO SANTIAGO, Johnson, C. R.

External publication

Si

Means

Linear Algebra Its Appl

Scope

Article

Nature

Científica

JCR Quartile

✓

SJR Quartile

✓

JCR Impact

0.973

SJR Impact

1.07

Web

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84964474465&doi=10.1016%2fj.laa.2016.04.021&partnerID=40&md5=34d6e31c84c9edbc1cc1278e9c89a4d2

Publication date

15/09/2016

ISI

000378464500001

Scopus Id

2-s2.0-84964474465

DOI

10.1016/j.laa.2016.04.021

Abstract

If T is a labelled tree, a matrix 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. (C) 2016 Elsevier Inc. All rights reserved.

Keywords

Graph; Neumaier conclusion; Spectral theory; Sylvester's identity; Totally positive matrix; Totally positive relative to a tree

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