Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrix A is given, and the statistician wants to compute the pth power of A, where p is a fractional or negative number; that is, a matrix R, such that R1/p = A. He can often get a satisfactory approximation to Ap by using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.