Axis Journal of Mathematical Statistics and Modelling
Matrix Operations Algorithm for Matrix-by-Matrix Division: Concepts, Possibilities, and Limitations
Abstract
Enyi Patrick Enyi
Matrix operations constitute a foundational component of linear algebra with wide applications in economics, engineering, statistics, accounting and finance, and other computational sciences. While operations such as addition, subtraction, and multiplication are well-defined, the notion of matrix-by-matrix division remains conceptually problematic. This paper examines standard matrix operations using a suite of sampled matrix arrays and provides a detailed analytical treatment of the concept of matrix division. It explores whether division between matrices is feasible, the conditions under which it may be interpreted, and the mathematical structures—such as matrix inverses and generalized inverses—that substitute for direct division. The study concludes that true matrix division is not defined in the conventional sense but can be meaningfully represented through multiplication by inverses under strict conditions guided by well-defined algorithmic steps.