OAI.MatrixMultiplication.complex_alpha_gt_93_div_200

The theorem states that the complex dual matrix multiplication exponent complexAlpha is strictly greater than 93/200. Here complexAlpha is defined as the supremum of the set of real k in the closed interval [0,1] for which rectangularOmega over the complex numbers equals 2. The quantity rectangularOmega(ℂ,k) is the infimum of all exponents τ that are admissible for multiplying an n × ⌈n^k⌉ matrix by an ⌈n^k⌉ × n matrix over ℂ. A real τ is admissible when, for every ε > 0, there is a constant C > 0 such that for every n ≥ 1 some correct straight-line arithmetic program computes the product of all such matrices using at most C·n^(τ+ε) gates, where constants and inputs cost nothing and each addition, subtraction or multiplication of earlier registers costs one. Equivalently, some k in [0,1] with k > 93/200 has rectangularOmega(ℂ,k) = 2.