Sufficient conditions to be exceptional

Authors

Robert B. Reams
Charles R. Johnson, William & Mary

Document Type

Article

Department/Program

Mathematics

Journal Title

Special Matrices

Pub Date

2016

Volume

4

Issue

1

First Page

67

Abstract

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).

Recommended Citation

Reams, Robert B. and Johnson, Charles R., Sufficient conditions to be exceptional (2016). Special Matrices, 4(1), 67-72.
10.1515/spma-2016-0007

DOI

10.1515/spma-2016-0007