Multidimensional Matrix Algebra Versus Tensor Algebra or μ > 0

Abstract

The paper compares of the multidimensional matrix algebra and the tensor algebra. It is shown that tensor algebra operations are realized in the multidimensional matrix algebra more efficiently. Examples are given to illustrate this fact. It is concluded that the multidimensional matrix algebra is a natural generalization of the tensor algebra. It is shown how the operation of the multiplication of multidimensional matrices is parallelized. It is said which data processing tasks are effectively formalized and implemented in the multidimensional matrix algebra. The paper was written in order to make the algebra of multidimensional matrices accessible to many software developers.