🚀 go-pugleaf

In <1gq7rgINNcqk@agate.berkeley.edu>
	shein@nima.berkeley.edu (Soren Hein) writes:

>Given a matrix X (M by N) of stochastic variables, find two matrices 
>A (M by M) and B (N by N) such that for the transformed matrix
>        Y = A X B,  
>we have
>        E[Y Y^T] = I_M
>        E[Y^T Y] = I_N

I'm not sure it can be done.  If you can settle for diagonal matrices
instead of identities, a singular value decomposition (essentially)
will do the job.  I assume you know the covariance matrix of your
Xij's.

1) Restrict A and B to orthogonal matrices.  Then,
   Y Y^T =  A X X^T A^T  independent of B, and
   Y^T Y =  B^T X^T X B  independent of A.

2) Form the deterministic matrix E[X X^T] and diagonalize.
   The eigenvectors are the columns of A.

3) Form the deterministic matrix E[X^T X] and diagonalize.
   The eigenvectors are the rows of B.
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us