Gottfried Wrote:I've got a text of R. Aldrovandi, where he explains Bell- and Carleman-matrices in a very basic way,

Not only does he explain Carleman matrices, he also applies them to compute tetration (via what we call the diagonalization method).

Unfortunately he introduces more confusion as he (as he also stated in the beginning) uses the term Carleman matrix for the transpose of what usually (in the literature) is called Carleman matrix.

Thank you Gottfried for digging this out.