  We will introduce a cyclic derivative for fully (stably) matricial functions
and study its basic properties. In particular, we will show the Poincar\'{e}
lemma for stably matricial functions of certain classes. We will also position
Voiculescu's framework of fully matricial functions in the context of nc
functions due to Kaliuzhnyi-Verbovetskyi and Vinnikov in order to clarify the
relation between the present work and previous related works.

Operator Algebras