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Linear preservers of copositive matrices

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Resumo:An n-by-n real symmetric matrix is called copositive if its quadratic form is nonnegative on nonnegative vectors. Our interest is in identifying which linear transformations on symmetric matrices preserve copositivity either in the into or onto sense. We conjecture that in the onto case, the map must be congruence by a monomial matrix (a permutation times a positive diagonal matrix). This is proven under each of some additional natural hypotheses. Also, the into preservers of standard type are characterized. A general characterization in the into case seems di¢ cult, and examples are given. One of them provides a counterexample to a conjecture about the into preservers.
Autores principais:Furtado, Susana
Outros Autores:Johnson, C. R.; Zhang, Yulin
Assunto:Linear preserver Copositive matrix Standard form Monomial matrix Congruence Rank preserver 15A04 15A86 15B48
Ano:2021
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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