On constructing algebras of finite range

Abstract

In the paper, a subalgebra whose elements are square matrices with real entries having the same sum of row entries is extracted from a complete matrix algebra. Using classical methods of matrix theory, the properties of constructed algebra are studied. This algebra is endowed with a norm that makes it possible to construct of elements of analysis in it by means of the matrix analysis methods. A new class of algebras of finite range is constructed, namely, an algebra of hypercomplex numbers, which is isomorphic to the corresponding matrix algebra. Thus, the obtained results for the matrices can be transferred to the elements of the isomorphic algebra of finite range, i.e. hypercomplex numbers. This lead to defining the functions of hypercomplex variable.