(* 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 = True
An equation editor format is here if you can't read Mathematica:
http://www.youvan.com/Examples/Example_18._Rapid_PseudoInverse_for_Scroll_Matrices.html
I'm not really comfortable with this concept of algebra but the wikipedia article on "Singular Value Decomposition" (SVD) should give you what you're looking for: http://en.wikipedia.org/wiki/Singular_value_decomposition
http://en.wikipedia.org/wiki/Singular_value_decomposition
Pedro,
Thank you but those guys looked at it on a talk page and then deleted the equation for about the same reasons I am asking this question. That link through youvan.com is to Wikipedia.
Oh ok. I made quite a few wikipedia articles and their policy concerning new material (particularly in science) is very clear. Any statement challenged or likely to be challenged should come from a reliable source.
They do give a definition for what they consider to be a reliable source (http://en.wikipedia.org/wiki/Wikipedia:Verifiability#What_counts_as_a_reliable_source). For this very reason if a new equation is posted without any article or book supporting it is very likely it will be removed. Also those materials should have been peer-reviewed (somehow) in order to be accepted. This is why self-published material is generally not accepted as a reliable source.
All of this to support the fact that wikipedia does not publish original research (http://en.wikipedia.org/wiki/Wikipedia:No_original_research). Research gate, for example, would be a much better medium for that. In order to post new scientific material on wikipedia I would advise first to publish it in a peer-reviewed journal.
Evidently people that manage wikipedia content are like you and me and therefore prone to error, misjudgment or misinterpretation of that content. Altogether however I do understand why the rules exist and as far as I know they're pretty good guiding lines.
For the scientific consequences of your question I really could not state if the equation you've put here is new material (like a different approach for the same problem) or a derivation of an old one (same formula written in a way it's more handy in certain sciences like computer sciences) since as I said I'm not familiar with the concept. Be careful thought that using Mathematica code to state a new concept is highly compromising for a fair analysis due to inability of fellow scientists to read correctly that statement and due to particulars on that programming language that can somehow infer on the results of your proposal.
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