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THE EXPONENT OF MATRIX MULTIPLICATION
The Search for a Basis Algorithm and
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additions and subtractions Aggregating Table algebraic extension Algorithm 20.2 algorithm of rank apply Proposition approximation arbitrary arithmetical algorithms arithmetical operations as(A asymptotic bilinear algorithm bilinear mapping bilinear problem bilinear steps binary numbers bit-complexity bit-time bits throughout chopping coefficients commutative quadratic algorithm compare Remark Complexity computational problems Corollary correction terms defined Definition derive designate digraph entries error estimate evaluation Example exponent extended floating point identity implies inputs integers involved Kronecker product linear algebra linear equations linear forms linear operations lower bounds mapping Matrix Multiplication matrix products modulo monic polynomial mXnXp nonlinear nonscalar norm notation nXn matrix obtain output polynomials principal terms Proposition 2.2 q q q QR-factors recursive construction recursively improvable reduced represent result ring F Section Similarly Strassen's algorithm substitution tensor Theorem 2.1 Toeplitz matrix transformation trilinear aggregating trilinear form unitary matrix upper bounds variables vector X-algorithm x-variables