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.