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Perfect Copositive Matrices
In this paper we give a first study of perfect copositive $n \times n$ matrices. They can be used to find rational certificates for completely positive matrices. We describe similarities and differences to classical perfect, positive definite matrices. Most of the differences occur only for $n \geq...
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| Published in: | Communications in Mathematics 2023-07, Vol.31 (2023), Issue 2... |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Online Access: | Get full text |
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| Summary: | In this paper we give a first study of perfect copositive $n \times n$
matrices. They can be used to find rational certificates for completely
positive matrices. We describe similarities and differences to classical
perfect, positive definite matrices. Most of the differences occur only for $n
\geq 3$, where we find for instance lower rank and indefinite perfect matrices.
Nevertheless, we find for all $n$ that for every classical perfect matrix there
is an arithmetically equivalent one which is also perfect copositive.
Furthermore we study the neighborhood graph and polyhedral structure of perfect
copositive matrices. As an application we obtain a new characterization of the
cone of completely positive matrices: It is equal to the set of nonnegative
matrices having a nonnegative inner product with all perfect copositive
matrices. |
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| ISSN: | 2336-1298 2336-1298 |
| DOI: | 10.46298/cm.11141 |