  The algebra of supernatural matrices is a key example in the theory of
locally finite central simple algebras, which studied in a previous paper of
the authors (\cite{Local}). It is also a stand-alone object admits a rich study
and various connections to other fields. The goal of this paper is to expose
some new information about supernatural matrices, mainly in terms of the
"inner" ways to identify such algebras, and their appearance as minimal
solutions to equations of the form $M_n(A)\cong A$. Viewing a natural
representation of this algebra, we show that supernatural matrices generalize
both McCrimmon's deep matrices algebra and $m$-petal Leavitt path algebra. We
also study their simple representations.
