Hi,
Thanks for the reply and interest.
I think what you are trying to say is that, in terms of above notation,
q(i,j) = p(i,j)*s(i,i)*s(j,j)
This is what I did in the simulation I mentioned in the post.
I randomly generated a symmetric positive definite matrix, and scaled (s(i,i)>=1...
Assume P is a symmetric positive-definite matrix,
and S to be a diagonal matrix with all its diagonal elements being greater than 1.
Let Q = SPS
then is Q-P symmetric positive-definite ?
i.e.
are the eigen-values of Q greater than P element-wise? or eig(Q)>= eig(P) in non-negative...