Matrices of infinite dimensions and their applications

TL;DR

This paper develops a comprehensive and systematic theory of infinite matrices, expanding the foundational understanding of their properties and potential applications across various scientific fields.

Contribution

It introduces a complete and ordered theoretical framework for infinite matrices, filling gaps in existing research and providing a basis for future studies.

Findings

Established fundamental properties of infinite matrices

Provided a structured theoretical framework

Identified potential applications in science and mathematics

Abstract

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