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### Contents

INTRODUCTION | 1 |

THE EXPONENT OF MATRIX MULTIPLICATION | 7 |

The Search for a Basis Algorithm and | 18 |

Copyright | |

22 other sections not shown

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### Common terms and phrases

A-algorithm additions and subtractions Aggregating Table algebraic extension Algorithm 20.2 algorithm of rank apply Proposition APSD-problem arbitrary arithmetical algorithms arithmetical operations as(A asymptotic bilinear algorithm bilinear problem binary bits binary numbers bit-complexity bit-time bits throughout coefficients commutative quadratic algorithm compare Remark computational problems Corollary correction terms defined Definition derive designate Det(n digraph Disjoint domain entries error estimate evaluation Example exponent extended floating point Hereafter identity implies inputs integers involves Kronecker product latter linear algebra linear equations linear forms linear operations linearly independent lower bounds mapping Matrix Multiplication matrix products maximum MI(n modulo multiplication nonlinear nonscalar norm notation number of bit-operations nXn matrix obtain output polynomials principal terms Proposition 2.2 QR-factors radix point recursive construction reduced represent result ring F ring of constants Section Similarly Strassen's algorithm submatrix tensor Theorem Theorem 2.1 trilinear form unitary matrix upper bounds variables vector X-rank x-variables