Relationships between tropical eigenvectors and tropical fixed points of the group GL(2,\(\mathbb{R}\))

Abstract

The eigenvalues, eigenvectors and fixed points of matrices have many applications in various branches of science and many mathematical disciplines.  In this paper first we introduce the concept of tropical fixed points, then we calculate the tropical eigenvalues and tropical eigenvectors of GL(2,\(\mathbb{R}\)).  Furthermore we give relationships between tropical eigenvectors and tropical fixed points of GL(2,\(\mathbb{R}\)).