On the other hand, the reduced echelon form of a matrix with integer coefficients generally contains non-integer coefficients.
2.
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.
3.
Some authors use the term " Gaussian elimination " to refer only to the procedure until the matrix is in echelon form, and use the term "'Gauss-Jordan elimination "'to refer to the procedure which ends in reduced echelon form.
4.
We then can write BP = \ begin { pmatrix } I _ r & G \ \ 0 & 0 \ end { pmatrix }, which allows us to identify ( I _ r, G ) = FP, i . e . the nonzero r rows of the reduced echelon form, with the same permutation on the columns as we did for A.
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