>[V,lambda]=eig(Ruu);
>H=V*diag(sqrt(diag(lambda.^(-1))))*V';
Can anyone please tell me more about the matrix H?

By using the division what we are doing is normalizing the V matrix 
we use the eigen value matrix for this since they represent the modes
Hope this helps, 
Lalin 

Dear readers,

my question is on something that looks like a variation of the
Karhunen-Loeve Transform.

The normal Karhunen-Loeve Transform would be like this: for a signal u
of length L and an adaptive FIR filter of order M, we compute the
Autocorrelation Matrix and its eigenvectors.  In Matlab:

L=max(size(u));
ruu=xcorr(u,u)/L;
M=16;
Ruu=toeplitz(ruu(L:L+M-1)); % Correlation Matrix
[V,lambda]=eig(Ruu);

Then one can use the matrix V as the transformation matrix for the
transform-domain LMS algorithm.

Now I have found another variety of this:

H=V*diag(sqrt(diag(lambda.^(-1))))*V';

and use H as the transformation matrix.  This was also called
Karhunen-Loeve transform, but it obviously is something different.
However, it also seems to converge more quickly.  I don't see why,
though.  Can anyone please tell me more about the matrix H?