Positive polynomials and hyperdeterminants

Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient conditi...

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Detalles Bibliográficos
Autor principal: Cukierman, F.
Formato: JOUR
Materias:
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00100757_v58_n3_p279_Cukierman
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Sumario:Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices. © 2007 Universität de Barcelona.