Sufficient conditions to be exceptional

Sufficient conditions to be exceptional

A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-...

Full description

Bibliographic Details
Main Authors: Johnson Charles R., Reams Robert B.
Format: Article
Language:English
Published: De Gruyter 2016-01-01
Series:Special Matrices
Subjects:
copositive matrix
positive semidefinite
nonnegative matrix
exceptional copositive matrix
irreducible matrix
Online Access:http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0007/spma-2016-0007.xml?format=INT
Description
Summary:A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).
ISSN:2300-7451

Similar Items