last modified Aug 6, 1996

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Orbits of U(n,n) acting on Mn

Given x and y does there exist a linear fractional map F so that y = F(x)? Linear fractional means that

Also, we require the coefficient matrix and its adjoint

to satisfy


As usual we are willing to assume that all elements of our algebra are invertible. We wish to discover the classical solution to the orbit problem. It says (with lots of invertiblity conditions) that if there is a matrix w and an invertible matrix w such that


then y=F(x). Conversely, if y=F(x), then such a w and w exist.

What we would like to do is use NCAlgebra to discover this theorem. First we assume that the linear fractional F(x) exists, and we try to produce w and w.

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