ELA, Volume 9, pp. 32-41, April 2002, abstract.
On the mth roots of a complex matrix
Panayiotis J. Psarrakos
If an nxn 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, a new simple proof for the
Jordan canonical form of the root B is presented.
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...).