I investigate on the number t of real eigenvectors of a real symmetric tensor. In particular, given a homogeneous polynomial f of degree d in 3 variables, I prove that t is greater or equal than $$2c+1$$ 2 c + 1 , if d is odd, and t is greater or equal than $$\max (3,2c+1)$$ max ( 3 , 2 c + 1 ) , if d is even, where c is the number of ovals in the zero locus of f. About binary forms, I prove that t is greater or equal than the number of real roots of f. Moreover, the above inequalities are sharp for binary forms of any degree and for cubic and quartic ternary forms.
Bollettino dell'Unione Matematica Italiana – Springer Journals
Published: Jan 9, 2017
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