k-幂零矩阵的一个新性质

New Property of K-nilpotent Matrix

通过对幂零矩阵的性质进行探讨,得出了k-幂零矩阵的一条新性质——n阶k-幂零矩阵的秩的取值范围,并给出了定理的证明过程。

By discussing the properties of nilpotent matrix,and a new property of k-nilpotent matrix was obtained about the value range of rank of k-nilpotent matrix with ordern.At last,the proof of the theorem was given.