Computation of roots of real and complex matrices

An algorithm is presented in this paper by which the rth root of real or complex matrices can be found without the computation of the eigenvalues and eigenvectors of the matrix. All required computations are in the real domain. The method is based on the Newton-Raphson algorithm and is capable of finding roots even when the matrix is defective. Computing the root of a matrix from eigenvalues and eigenvectors would be the preferred method if these data were available.