(* complete dictionary of words, one per row, number of rows is (alpha^word), using words of length "word" and an alphabet of "alpha" number of characters *)
alpha = 4; word = 3; dict =.;
dict = Partition[Flatten[Tuples[Reverse[IdentityMatrix[alpha]], word]], (alpha*word)];
PseudoInverse[dict] == ((Transpose[dict])*((alpha)^-(word - 1))) - ((word - 1)/(alpha^word)/word)
Output is True
An equation editor format is here:
http://www.youvan.com/Examples/Example_18._Rapid_PseudoInverse_for_Scroll_Matrices.html
