Analyzing Invariance Properties - Reflector Matrices

In this section the reflector matrix corresponding to each type of discrepancy function will be defined, followed by a discussion of how these matrices may be used to analyze invariance properties. The abbreviated notation will use to stand for the reproduced covariance matrix .

The reflector matrices for the discrepancy functions analyzed here are






where the elements of the symmetric matrix Q are


where dij is the Kronecker delta,


and U is the weight matrix referred to in Equation 67.