USING MATRIX DIAGONALIZATION AND PYTHON TO STUDYING A BIDIMENSIONAL LINEAR DISCRETE MIGRATION MODEL

Abstract

This work was written for students of Mathematics, Biology, Physics, and Engineering. In the field of Linear Algebra, diagonalization is a powerful technique that simplifies matrix calculations by transforming a given matrix into a similar diagonal matrix. This method proves particularly useful for solving systems of linear equations, computing matrix powers, and analyzing the dynamics of linear systems. In this article, we explore a two-dimensional linear discrete model of rural-urban migration. We demonstrate how diagonalization can simplify the model and provide insights into migration patterns. Additionally, we employ Python to develop and analyze this bidimensional linear discrete model. Python's robust computational capabilities allow for complex simulations, which we use to validate the model and visualize migration patterns. The ability to create detailed graphics further aids in interpreting the results. Discrete models, in contrast to continuous ones, offer the distinct advantage of being more accessible for numerical exploration using calculators or computers (in our case, Python). This accessibility enhances the model's pedagogical value, allowing us to effectively demonstrate the connections between mathematical theory and real-world phenomena.

Keywords: Diagonalization; bidimensional Linear discrete dynamical system; real-world application.