1 dimensional example (cont.)
Diagonalizing U(m,n) determines the eigenvalues and
eigenvectors  of  U(m,n). The sum of the eigenvalues
is the trace of the U and is  an invariant corresponding
to the total variance. The diagonalization  breaks the variance
into independent pieces and the eigenvalue is the variance in
each independent piece. The eigenvectors are the spatial
structures corresponding to each independent variance
Eigenvectors are orthogonal and can be used as
                          a basis for u