However, the order in which the product is parenthesized affects the number of simple arithmetic operations needed to compute the product. ![]() ![]() For example, for four matrices A, B, C, and D, we would have: The matrix multiplication is associative as no matter how the product is parenthesized, the result obtained will remain the same. The problem is not actually to perform the multiplications but merely to decide the sequence of the matrix multiplications involved. ![]() Matrix chain multiplication (or Matrix Chain Ordering Problem, MCOP) is an optimization problem that to find the most efficient way to multiply a given sequence of matrices. ![]() Matrix chain multiplication problem: Determine the optimal parenthesization of a product of n matrices.
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