On the maximum rank of a real binary form
Abstract We show that a real binary form f of degree n has n distinct real roots if and only if for any $${(\alpha,\beta)\in\mathbb{R}^2{\setminus}\{0\}}$$ all the forms αfx + βfy have n − 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary fo...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Causa, A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Anmerkung: |
© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010 |
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| Übergeordnetes Werk: |
Enthalten in: Annali di matematica pura ed applicata - Springer-Verlag, 1858, 190(2010), 1 vom: 21. März, Seite 55-59 |
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| Übergeordnetes Werk: |
volume:190 ; year:2010 ; number:1 ; day:21 ; month:03 ; pages:55-59 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10231-010-0137-2 |
|---|
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On the maximum rank of a real binary form |
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Causa, A. |
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Annali di matematica pura ed applicata |
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Causa, A. Re, R. |
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10.1007/s10231-010-0137-2 |
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510 |
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on the maximum rank of a real binary form |
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On the maximum rank of a real binary form |
| abstract |
Abstract We show that a real binary form f of degree n has n distinct real roots if and only if for any $${(\alpha,\beta)\in\mathbb{R}^2{\setminus}\{0\}}$$ all the forms αfx + βfy have n − 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909.4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has n distinct real roots. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010 |
| abstractGer |
Abstract We show that a real binary form f of degree n has n distinct real roots if and only if for any $${(\alpha,\beta)\in\mathbb{R}^2{\setminus}\{0\}}$$ all the forms αfx + βfy have n − 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909.4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has n distinct real roots. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010 |
| abstract_unstemmed |
Abstract We show that a real binary form f of degree n has n distinct real roots if and only if for any $${(\alpha,\beta)\in\mathbb{R}^2{\setminus}\{0\}}$$ all the forms αfx + βfy have n − 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909.4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has n distinct real roots. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010 |
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On the maximum rank of a real binary form |
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