ABSTRACT
A canonical form of a matrix is a special form with the properties that every matrix is associated to a matrix in that form (the canonical form of the matrix), it is unique or essentially unique (typically up to some type of permutation), and it has a particularly simple form (or a form well suited to a specific purpose). A canonical form partitions the set matrices in F m×n into sets of matrices each having the same canonical form, and that canonical form matrix serves as the representative. The canonical form of a given matrix can provide important information about the matrix. For example, reduced row echelon form (RREF) is a canonical form that is useful in solving systems of linear equations; RREF partitions F m×n into sets of row equivalent matrices.
