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.File in questo prodotto:
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