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MATRICES TOTALLY POSITIVE RELATIVE TO A TREE

Authors

Johnson, Charles R. , COSTAS SANTOS, ROBERTO SANTIAGO, Tadchiev, Boris

External publication

Si

Means

Electron J. Linear Algebra

Scope

Article

Nature

Científica

JCR Quartile

✗

SJR Quartile

✓

JCR Impact

0.892

SJR Impact

0.981

Web

https://www.scopus.com/inward/record.uri?eid=2-s2.0-65749091058&doi=10.13001%2f1081-3810.1306&partnerID=40&md5=04326a2e75f0d955202c715366e91896

Publication date

01/04/2009

ISI

000265108300001

Scopus Id

2-s2.0-65749091058

DOI

10.13001/1081-3810.1306

Abstract

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.

Keywords

Totally positive matrices; Sylvester's identity; Graph theory; Spectral theory

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