 For instance, it is a fact from matrix theory that every non-singular "T" has a logarithm "S" in the sense that "eS" = "T".It is desirable to have a functional calculus that allows one to define, for a non-singular "T", ln("T") such that it coincides with "S".This can not be done via power series, for example the logarithmic series

converges only on the open unit disk.