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Matrices are very popular and widely used in mathematics and other fields ofscience. Every mathematician has known the properties of finite-sized matricessince the time of study. In this paper, we consider the basic theory of infnitematrices. So far, there have been references and few results in certainscientific fields, but they have not been thoroughly researched. This paperpresents a complete possible and ordered theory of infinite matrices.

Matrices of infinite dimensions and their applications