Classification of Canonical Bases for (n−1)−dimensional Subspaces of n− Dimensional Vector Space

Canonical bases for (n-1)-dimensional sub spaces of n-dimensional vector space are introduced and classified in the article. This result is very prospective to utilize canonical bases at all applications. For example, maximal sub algebras of Lie algebras can be found using them.

The canonical bases for (n-1)-dimensional sub spaces of n− dimensional vector space are introduced in the article, and all non equivalent of them are classified (Theorem 2). This result generalizes a particular result for 5-dimensional sub spaces of 6-dimensional vector space obtained in the previous article of the same author.To analyze the general case, reduced row echelon forms of matrices are utilized; about reduced row echelon forms. In addition to the principal result, all non-equivalent reduced row echelon forms for (n−1)×n matrices of the rank (n−1) are found.