Sufficient conditions to be exceptional

Special Matrices

Johnson Charles R.¹  Reams Robert B.² 

[1] Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187;Department of Mathematics, SUNY Plattsburgh, 101 Broad Street, Plattsburgh, NY 12901;

关键词: copositive matrix;    positive semidefinite;    nonnegative matrix;    exceptional copositive matrix;    irreducible matrix;   

DOI  :  10.1515/spma-2016-0007

来源: DOAJ

【 摘 要 】

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).

【 授权许可】

Unknown