a couple extra thoughts/questions..
I am aware that if you have a square matrix, H, and you row reduce the augmented matrix <H|I> You return with <I|InverseH>
is there a result for non square matrices?
And is there a result if you perform this with a non square matrix and its transpose - are the reults related?.
and what about if you carry this out on H . Transpose(H)
and then Transpose(H) . H of course these are square so you will end up with the inverse of each, but are these inverses related?