Extremal copositive matrices with minimal zero supports of cardinality two

Roland Hildebrand

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arXiv · 1707.08862

Extremal copositive matrices with minimal zero supports of cardinality two

Roland Hildebrand

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Abstract

Let $A \in {\cal C}^n$ be an extremal copositive matrix with unit diagonal. Then the minimal zeros of $A$ all have supports of cardinality two if and only if the elements of $A$ are all from the set $\{-1,0,1\}$. Thus the extremal copositive matrices with minimal zero supports of cardinality two are exactly those matrices which can be obtained by diagonal scaling from the extremal $\{-1,0,1\}$ unit diagonal matrices characterized by Hoffman and Pereira in 1973.

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Roland Hildebrand. 2017-07-27. Extremal copositive matrices with minimal zero supports of cardinality two. https://arxiv.org/abs/1707.08862

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