Canonical matrices with entries integers modulo p
Abstract
The work considers an equivalence relation in the set of all n× m matrices with entries in the set [p]=\ 0,1,… , p-1 \. In each element of the factor-set generated by this relation, we define the concept of canonical matrix, namely the minimal element with respect to the lexicographic order. We have found a necessary and sufficient condition for an arbitrary matrix with entries in the set [p] to be canonical. For this purpose, the matrices are uniquely represented by ordered n-tuples of integers.
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