Abstract: A computer system is configured to create a product matrix of data from two matrices of data through the use of a representation in a group algebra. The matrices are represented in a group algebra based on a mathematical group adhering to certain criteria. Then the representations are mapped to vectors in a multidimensional vector space where their product can be obtained by reduction into a block-diagonal matrix multiplication which can be recursively computed by the same process. Multiple matrix multiplications can also be performed simultaneously though selection of a group which satisfies certain properties. Through this process, computational time improvements are obtained.