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, if d is odd, and t is greater or equal than max(3, 2c + 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.
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