Maximum relative distance between real rank-two and rank-one tensors

Abstract It is shown that the relative distance in Frobenius norm of a real symmetric order- d tensor rank-two to its best rank-one approximation upper bounded by $$\sqrt{1-(1-1/d)^{d-1}}$$ 1 - ( / d ) . This achieved determining minimal possible ratio between spectral and for tensors border rank two, which equals $$\left( 1-{1}/{d}\right) ^{(d-1)/{2}}$$ 2 These bounds are also verified arbitrary reducing case.