ECHELON (matrix) ;
The ECHELON function uses elementary row operations to reduce a matrix to row-echelon normal form, as in the following example (Graybill, 1969):
a = {3 6 9,
1 2 5,
2 4 10 };
e = echelon(a);
print e;
Figure 23.101: Result of the ECHELON Function
| e | ||
|---|---|---|
| 1 | 2 | 0 |
| 0 | 0 | 1 |
| 0 | 0 | 0 |
If the argument is a square matrix, then the row-echelon normal form can be obtained from the Hermite normal form by rearranging rows that are all zeros. See the HERMITE function for details about the Hermite normal form.