ELA ON THE m th ROOTS OF A COMPLEX MATRIX
نویسنده
چکیده
Abstract. If an n× n complex matrix A is nonsingular, then for every integer m > 1, A has an mth root B, i.e., Bm = 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 Ak (k = 0, 1, 2, . . .).
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