This paper is concerned with the unitary interactor matrix and its role in the explicit solution of the minimum variance and singular LQ output feedback control problems. The unitary interactor matrix, an all-pass factor that factors the infinite zeros while keeping the spectrum of the underlying system unchanged, is also extended to include the weighted unitary interactor matrix. With the weighted unitary interactor matrix, the multivariate minimum variance control law as proposed by Goodwin and Sin (1984) is shown to be pairing-invariant and identical to the singular LQ output feedback control law.