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arXiv · 2310.09841

Differential calculus for fully matricial functions I

Hyuga Ito
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Abstract

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.

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Hyuga Ito. 2023-10-15. Differential calculus for fully matricial functions I. https://arxiv.org/abs/2310.09841

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