Iteration exercises: f(x)=1/(1+x)

[bo198214]

regular iterations at n fixed points correspond when the function can be represented by an n x n matrix with real or positive real entries.
...
if i recall correctly ...

Recall from where? I dont know about other finite matrix representations than those 2x2 of linear fractions (but was wondering whether it exists). Matrix representation \( M_f \) in the sense that \( M_{f\circ g}=M_f M_g \). For example which kind of function is representable with 3x3 matrices?