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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 16, 2015

Sufficient conditions to be exceptional

  • Charles R. Johnson and Robert B. Reams EMAIL logo
From the journal Special Matrices


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).


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Received: 2015-4-22
Accepted: 2015-11-12
Published Online: 2015-12-16
Published in Print: 2016-1-1

© 2016 Charles R. Johnson et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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