Some theorems about matrix multiplication
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This paper considers the computation of matrix chain products of the form M1 × M2 ×...× Mn-1. If the matrices are of different dimensions, the order in which the matrices are computed affects the number of operations. An optimum order is an order which minimizes the total number of operations. We present some theorems about an optimum order of computing the matrices. Based on these theorems, an O(n log n) algorithm for finding the optimum order is presented.
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