摘要
该文给出了用初等因子求矩阵乘幂的秩及其指标的简捷方法,由此提出了矩阵乘幂的秩谱及其分界秩的概念,并初步讨论了这一秩谱的基本性质,进而又给出了已知矩阵的乘幂的秩求矩阵的初等因子及其矩阵的方法。
In this paper, a simple way is given to find the rank of matrixpower and its index by elementary divisor. The paper gives the idea of randspectrum of matrix power and its dividing rank, and then discusses the ele-mentary quality of rank spectrum. The inverse problem is also discussed.
关键词
秩
矩阵乘幂
指标
秩谱
幂零阵
rank
matrix power
index
rank sepctrum of matrix power
nilpotent matrix
