Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrixAis given, and the statistician wants to compute thepth power ofA, wherepis a fractional or negative number; that is, a matrixR, such thatR1/p=A. He can often get a satisfactory approximation toApby using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.