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

(148)

(149)

(150)

(151)

(152)

where the elements of the symmetric matrix Q are

(153)

where dij is the Kronecker delta,

(154)

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