A (5/2)n2-Lower Bound for the Multiplicative Complexity of n×n-Matrix Multiplication
نویسنده
چکیده
We prove a lower bound of 5 2 n 2 ? 3n for the multiplicative complexity of n n{matrix multiplication over arbitrary elds. More general, we show that for any nite dimensional semisimple algebra A with unity, the multiplicative complexity of the multiplication in A is bounded from below by 5 2 dim A ? 3(n1 + + nt) if the decomposition of A = A1 At into simple algebras A = D n n contains only noncommutative factors, that is, the division algebra D is noncommu-tative or n 2.
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