Some observations on the Youla form and conjugate-normal matrices

Two square complex matrices A, B are said to be unitarily congruent if there is a unitary matrix U such that A = UBUT. The Youla form is a canonical form under unitary congruence. We give a simple derivation of this form using coninvariant subspaces. For the special class of conjugate-normal matrices the associated Youla form is discussed.