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-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-01-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0007/spma-2016-0007.xml?format=INT |
| _version_ | 1818576958111350784 |
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| author | Johnson Charles R. Reams Robert B. |
| author_facet | Johnson Charles R. Reams Robert B. |
| author_sort | Johnson Charles R. |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-12-16T06:22:17Z |
| format | Article |
| id | doaj.art-b46d4299822249b196efee05af64d597 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-16T06:22:17Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-b46d4299822249b196efee05af64d5972022-12-21T22:41:06ZengDe GruyterSpecial Matrices2300-74512016-01-014110.1515/spma-2016-0007spma-2016-0007Sufficient conditions to be exceptionalJohnson Charles R.0Reams Robert B.1Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187Department of Mathematics, SUNY Plattsburgh, 101 Broad Street, Plattsburgh, NY 12901A 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).http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0007/spma-2016-0007.xml?format=INTcopositive matrixpositive semidefinitenonnegative matrixexceptional copositive matrixirreducible matrix |
| spellingShingle | Johnson Charles R. Reams Robert B. Sufficient conditions to be exceptional Special Matrices copositive matrix positive semidefinite nonnegative matrix exceptional copositive matrix irreducible matrix |
| title | Sufficient conditions to be exceptional |
| title_full | Sufficient conditions to be exceptional |
| title_fullStr | Sufficient conditions to be exceptional |
| title_full_unstemmed | Sufficient conditions to be exceptional |
| title_short | Sufficient conditions to be exceptional |
| title_sort | sufficient conditions to be exceptional |
| topic | copositive matrix positive semidefinite nonnegative matrix exceptional copositive matrix irreducible matrix |
| url | http://www.degruyter.com/view/j/spma.2016.4.issue-1/spma-2016-0007/spma-2016-0007.xml?format=INT |
| work_keys_str_mv | AT johnsoncharlesr sufficientconditionstobeexceptional AT reamsrobertb sufficientconditionstobeexceptional |