ABSTRACT
Let S=<yyt> be the covariance matrix of y; N=<nnt>is the covariance matrix of the noise. The covariance matrix of y' is
The terms proportional to <ynt> are zero, since we assume that the noise is uncorrelated with the signal y. In component notation, denoting the components of Sy' by sij,
Therefore,
The covariance matrix of any set of measurements that include uncorrelated noise will have the form of equation (131). As I said in the last section, we want to choose basis vectors so that the eigenvalues of Sy
' are the sum of the eigenvalues of Sy and the eigenvalues of N:
where ?i and µi are the eigenvalues of S and N respectively , and the eigenvalues
of . How can we accomplish this?
