The Order of Algebraic Linear Transformations

In this paper we extend the results of an earlier note [1].Definition. Let E be an extension field of the rationals. A vector v = (b1, …, bn) in En is algebraic if each coordinate bi is algebraic over the rationals. A linear transformation T: En → En is algebraic if T(v) is an algebraic vector for every algebraic vector v.Definition. The degree of an algebraic linear transformation T, denoted by deg T, is the minimum of [K:Q] taken over all finite algebraic extensions K of the rationals Q such that T: Kn → Kn.