Language Reference

ECHELON Function

reduces a matrix to row-echelon normal form

ECHELON( matrix)

where matrix is a numeric matrix or literal.

The ECHELON function uses elementary row operations to reduce a matrix to row-echelon normal form, as in the following example (Graybill 1969, p. 286):

  
       a={3  6  9, 
          1  2  5, 
          2  4 10}; 
       e=echelon(a);
 

The resulting matrix is as follows:

  
                 E             3 rows      3 cols    (numeric) 
  
                                 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.