We determine the rank of a general real binary form of degree d=4 or d=5. In the case d=5, the possible values of the rank of such general forms are 3, 4, and 5. This is the first reported case, to our knowledge, where more than two typical ranks have been found. We prove that a real binary form of degree d with d real roots has rank d.

On the typical rank of real binary forms / Pierre, Comon; Ottaviani, GIORGIO MARIA. - In: LINEAR & MULTILINEAR ALGEBRA. - ISSN 0308-1087. - STAMPA. - 60:(2012), pp. 657-667. [10.1080/03081087.2011.624097]

On the typical rank of real binary forms

OTTAVIANI, GIORGIO MARIA
2012

Abstract

We determine the rank of a general real binary form of degree d=4 or d=5. In the case d=5, the possible values of the rank of such general forms are 3, 4, and 5. This is the first reported case, to our knowledge, where more than two typical ranks have been found. We prove that a real binary form of degree d with d real roots has rank d.
2012
60
657
667
Pierre, Comon; Ottaviani, GIORGIO MARIA
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/588713
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