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

Si

Linear Alg. Appl.

Article

Científica

1

1

0.973

1.07

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

15/09/2016

000378464500001

2-s2.0-84964474465

10.1016/j.laa.2016.04.021

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.

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

• ROBERTO SANTIAGO COSTAS SANTOS