Classification of Canonical Bases for (n-2)-Dimensional Subspaces of n-Dimensional Vector Space

Abstract

Famous K. Gauss introduced reduced row echelon forms for matrices approximately 200 years ago to solve systems of linear equations but the number of them and their structure has been unknown until 2016 when it was determined at first in the previous article given up to (n−1)×n matrices. The similar method is applied to find reduced row echelon forms for (n−2)×n matrices in this article, and all canonical bases for (n−2)-dimensional subspaces of -dimensional vector space are found also.