Similarly, a system of equations is said to be in " reduced row echelon form " or in " canonical form " if its augmented matrix is in reduced row echelon form.
32.
To put an " n " by " n " matrix into reduced echelon form by row operations, one needs n ^ 3 arithmetic operations; which is approximately 50 % more computation steps.
33.
For example, Jordan normal form is a canonical form for matrix similarity, and the row echelon form is a canonical form, when one considers as equivalent a matrix and its left product by an invertible matrix.
34.
For a given matrix, despite the row echelon form not being unique, all row echelon forms and the reduced row echelon form have the same number of zero rows and the pivots are located in the same indices.
35.
For a given matrix, despite the row echelon form not being unique, all row echelon forms and the reduced row echelon form have the same number of zero rows and the pivots are located in the same indices.
36.
For a given matrix, despite the row echelon form not being unique, all row echelon forms and the reduced row echelon form have the same number of zero rows and the pivots are located in the same indices.
37.
Reduced row echelon form is what I was thinking of, and the related Gaussian elimination seems to be a close corollary to the process I am writing, and therefore a suitable name for the method in my code.
38.
What are the practical uses of row echelon form ( which I barely remember studying back in high school but, for some reason, was thinking about today ) ? talk ) 16 : 22, 30 March 2011 ( UTC)
39.
In fact, the computation may be stopped as soon as the upper matrix is in column echelon form : the remainder of the computation consists in changing the basis of the vector space generated by the columns whose upper part is zero.
40.
Once all of the leading coefficients ( the left-most non-zero entry in each row ) are 1, and every column containing a leading coefficient has zeros elsewhere, the matrix is said to be in reduced row echelon form.
