幂零矩阵的m次根

摘要

This paper is derived to the study of the equation Xm=A where A is a n×n nilpotent matrix with 2≤m∈N. We can derive some good relationship between the characters of A and unsolvability of the equation Xm=A.%主要研究当A是幂零矩阵时,方程Xm=A的性质.我们可以得到一些关于方程Xm=A无解性与A自身的特点之间的关系.