A Gauche perspective on row reduced echelon form and its uniqueness

Abstract

Using a left-to-right "sweeping" algorithm, we define the \emph{Gauche basis} for the column space of a matrix $M$. By means of the Gauche basis we interpret the row reduced echelon form of $M$, and give a direct proof of its uniqueness. We conclude with pedagogical reflections.

12 pages, 1 figure ; added motivational discussion, section on geometric interpretation, more references ; added dedication