Full rank factorization and the Flanders Theorem

Abstract

In this paper, a method is given that obtains a full rank factorization of a rectangular
matrix. It is studied when a matrix has a full rank factorization in echelon form. If this factorization exists, it is proven to be unique. Applying the full rank factorization in echelon form the Flanders theorem and its converse in a particular case are proven.