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Multi-matrices and arithmetical operations with multi-matrices

The multi-space structure has been defined by Fl Smarandache as a union spaces with some additional conditions hold. The mathematician L. Mao wrote a series of works in which he introduces the concepts of multi-group, multi-ring, multivector - space etc. In [1] (Smarandache Multi-Space Theory (I)), at open problems section, he suggests the introduction of a theory of matrices and applications defined on the multi-linear spaces. This paper will give an example of a multi-ring structure, introduces the notion of multi-matrix and defines the multi-matrix addition and multiplication.