# Chain Matrix Multiplication

From Algorithmist

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Problem definition: Evaluation of the product of n matrices M1, M2, .... , Mn

1. Multiplication of Matrix : Two matrices could only be multiplied if they have a common dimension value. For example to multiply M×N, where matrix M is a×b and matrix N is b×c, takes abc operations. Without this common dimension b between them it would not be possible for them to be multiplied. Matrix multiplication is associative, but not commutative : N×M might not equal M×N and, in fact, N×M might not even be defined because of a lack of common dimension. The order of which matrices are multiplied together first can significantly affect the time required.