ABSTRACT
There is a unitary matrix U that diagonalizes Sx=<xx t>, just as we diagonalized B in
equation (88). For any n×n matrix U and vectors p and q of length n, (Up)(Up)t=U (pqt)U t, as we can easily prove by writing it in component notation. Define v=Ux. The covariance matrix of v is a diagonal matrix USU t=D. This transforms the basis vectors so that the components of v vary independently. We shall make use of this property shortly.
