
14 Algebraic Operads: An Algorithmic Companion
Recall that the row canonical form of a matrix A, is a matrix R obtained
from A by elementary row operations for which the first nonzero entry of each
nonzero row of R is equal to 1 (this entry is called the pivot of that row), the
positions of the pivots increase with the increase in the row number, and all
entries in each column containing a pivot are equal to zero.
The following algorithm for computing canonical forms of matrices is well-
known. (This algorithm is recursive in the number of rows of the matrix.)
Algorithm 1.2.1.7 (Row canonical form computation).
Input: A m × n-matrix A = [a
ik
]
1≤i≤m,1