Artículo
Cukierman, F. "Positive polynomials and hyperdeterminants" (2007) Collectanea Mathematica. 58(3):279-289
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Positive polynomials and hyperdeterminants |
| Autor: | Cukierman, F. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina |
| Palabras clave: | Characteristic polynomial; Discriminant; Hyperdeterminant; Positive |
| Año: | 2007 |
| Volumen: | 58 |
| Número: | 3 |
| Página de inicio: | 279 |
| Página de fin: | 289 |
| Título revista: | Collectanea Mathematica |
| Título revista abreviado: | Collect. Math. |
| ISSN: | 00100757 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman |
Referencias:
- Blekherman, G., Convexity properties of the cone of nonnegative polynomials (2004) Discrete Comput. Geom, 32, pp. 345-371
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- Dold, A., (1980) Lectures on Algebraic Topology, , Springer-Verlag, Berlin-New York
- Dolgachev, I., Lectures on Invariant Theory (2003) London Mathematical Society Lectures Notes Series, 296. , Cambridge University Press
- Fulton, W., Harris, J., (1991) Representation Theory, , Springer-Verlag, New York
- Gantmacher, F.R., (1998) The Theory of Matrices, , AMS Chelsea Publishing, Providence, RI
- Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V., Hyperdeterminants (1992) Adv. Math, 96, pp. 226-263
- Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V., (1994) Discriminants, Resultants and Multidimensional Determinants, , Birkhäuser Boston, Inc, Boston, MA
- Godement, R., (1958) Topologie Algebrique et Theorie des Faisceaux, , Hermann, Paris
- Kaplansky, I., Hilbert's Problems (1977) Lecture Notes-University of Chicago
- Pfister, A., Hilbert's Seventeenth Problem and Related Problems on Definite Forms (1974) Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math. 28, Northern, , Illinois, Amer. Math. Soc, Providence, RI
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- Reznick, B., Sums of even powers of real linear forms (1992) Mem. Amer. Math. Soc, 96, pp. 8-155
Citas:
---------- APA ----------
(2007) . Positive polynomials and hyperdeterminants. Collectanea Mathematica, 58(3), 279-289.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman [ ]
---------- CHICAGO ----------
Cukierman, F. "Positive polynomials and hyperdeterminants" . Collectanea Mathematica 58, no. 3 (2007) : 279-289.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman [ ]
---------- MLA ----------
Cukierman, F. "Positive polynomials and hyperdeterminants" . Collectanea Mathematica, vol. 58, no. 3, 2007, pp. 279-289.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman [ ]
---------- VANCOUVER ----------
Cukierman, F. Positive polynomials and hyperdeterminants. Collect. Math. 2007;58(3):279-289.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman [ ]
