The problem of the decomposition of data z ∈ IRT into several components xi ∈ IRT via the minimization of a sum of quadratic forms x’Aix is considered. The resulting transformations of z onto the optimal components are linear and diagonalizable with eigenvalues in the unit interval, which characterizes the transformations as smoothers. Principles of constructing quadratic forms are presented and especially the effect of using cyclic quadratic forms is examined.