On the m-th roots of a complex matrix
Panayiotis Psarrakos · Electronic Journal of Linear Algebra · 2002
If an n × n complex matrix A is nonsingular, then for every integer m > 1, A has an mth root B, i.e., B m = A. In this paper, we present a new simple proof for the Jordan canonical form of the root B.Moreover, a necessary and sufficient condition for the existence of mth roots of a singular complex matrix A is obtained.This condition is in terms of the dimensions of the null spaces of the powers A k (k = 0, 1, 2, . ..).