 More precisely, the functional calculus defines a continuous algebra homomorphism from the holomorphic functions on a neighbourhood of the spectrum of "T" to the bounded operators.This article will discuss the case where "T" is a bounded linear operator on some Banach space.In particular, "T" can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction.