Let \(f\) be a convergent power series over \(\mathbb{C}\). The author studies some explicit forms for functions of matrices. For example it is shown that \(f(tA)=f(t)\diamondsuit(I-tA)^{-1}\), where \(t\in\mathbb{C}\), \(w^*(t)\neq 0\), \(w^*\) is the reversal of the characteristic polynomial of \(A\) (i.e. \(w(t)=\det(tI-A)\) and \(w^*(t)=t^nw(t^{-1})\) for \(n\times n\) matrix \(A\)) and \(\diamondsuit\) denotes the Hadamard product of two power series (i.e. \(g(t)\diamondsuit h(t)=\sum g_nh_nt^n\) if \(g(t)=\sum g_nt^n\) and \(h(t)=\sum h_nt^n\)).