CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Matrix chain multiplication (or Matrix Chain Ordering Problem, MCOP) is an optimization problem that can be solved using dynamic programming . Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices . The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved. We have many options because matrix multiplication is associative . In other words, no matter how we parenthesize the product, the result obtained will remain the same. For example, if we had four matrices A , B , C , and D , we would have: (( AB ) C ) D = (( A ( BC )) D ) = ( AB )( CD ) = A (( BC ) D ) = A ( B ( CD )). However, the order in which we parenthesize the product affects the number of simple arithmetic ...