Prove
Lemma 2 ([Detecting characters]). Let d≥2 and k≥0 be integers with k<d^ν ,…Definition 1. A tensor character is an additive, multiplicative,…Proposition
This is the interpolation passage from approximate to exact bilinear algorithms~, applied to characters. Let F()=B+ F_1+⋯+^L F_L be the transformed tensor. For each nonzero , it is a restriction of A . The polynomial F()^ ⊗j has degree at most jL and constant coefficient B^ ⊗j . Interpolation at jL+1 distinct nonzero points writes this coefficient as a linear combination of specializations. A linear combination of tensors on common spaces is a restriction of their full direct sum: identify the corresponding variables and absorb each scalar coefficient into one leg. Therefore λ(B)^j≤(jL+1)λ(A)^j. Taking j th roots and letting j→∞ proves the result. The degeneration, and hence L , is fixed during this limit.