Eigen-concepts in the multiplicative linear algebra context

Abstract

The concept of eigenvalues is associated with the linearity one, through the structure of vectorial space. The multiplicative linear algebra is a structure in which an expression such as x^3y^2 can be considered a linear combination of variables x and y. This article is reserved to show the corresponding analogues for an Eigenvalue Theory. We exemplify its applications by introducing a connection with the analysis of a nonlinear dynamical system in the standard sense, although a linear recurrence in the multiplicative one.El concepto de valores propios está asociado al de linealidad, a través de la estructura del espacio vectorial. El álgebra lineal multiplicativa es una estructura en la que una expresión como x^3y^2 puede ser considerada una combinación lineal de las variables x y y. Este artículo está destinado a mostrar los análogos correspondientes para una teoría de valores propios en este contexto. Se ejemplifican sus aplicaciones mediante la introducción de una conexión con el análisis de un sistema dinámico no lineal en el sentido estándar, aunque con una recurrencia lineal en el marco multiplicativo.The concept of eigenvalues is associated with the linearity one, through the structure of vectorial space. The multiplicative linear algebra is a structure in which an expression such as x^3y^2 can be considered a linear combination of variables x and y. This article is reserved to show the corresponding analogues for an Eigenvalue Theory. We exemplify its applications by introducing a connection with the analysis of a nonlinear dynamical system in the standard sense, although a linear recurrence in the multiplicative one