Some Basic Facts about Linear Algebra over $\mathbb{G}\mathbb{F}$(2)

Abstract

The purpose of this chapter is to identify some facts about $\mathbb{G}\mathbb{F}$(2)-vector spaces and about matrices over $\mathbb{G}\mathbb{F}$(2). To emphasize the differences between matrices over ℙ, or ℂ, and matrices over $\mathbb{G}\mathbb{F}$(2), we note several interesting phenomena. The contents of this chapter are already known, but we present them here as a “warm up.” They are stated here so that they can be used elsewhere, and for background.