On the typical rank of real binary forms

Pierre Comon (1) , Giorgio Ottaviani (2)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
2 Dipartimento di Matematica "Ulisse Dini"

We determine the rank of a general real binary form of degree d=4 and d=5. In the case d=5, the possible values of the rank of such general forms are 3,4,5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.

Domaines: Géométrie algébrique [math.AG]; Statistiques [math.ST]; Théorie [stat.TH]

Pierre Comon, Giorgio Ottaviani. On the typical rank of real binary forms. Linear and Multilinear Algebra, 2012, 60 (6), pp.657-667. ⟨10.1080/03081087.2011.624097⟩. ⟨hal-00420415v1⟩