  Certain upper triangular matrices, termed as Parikh matrices, are often used
in the combinatorial study of words. Given a word, the Parikh matrix of that
word elegantly computes the number of occurrences of certain predefined
subwords in that word. In this paper, we compute the Parikh matrix of any word
raised to an arbitrary power. Furthermore, we propose canonical decompositions
of both Parikh matrices and words into normal forms. Finally, given a Parikh
matrix, the relation between its normal form and the normal forms of words in
the corresponding M-equivalence class is established.
