本质(m,l)幂等矩阵的特征研究

Studies on Character of Essential(m,l) Idempotent Matrix

若有最小正整数m使当m>l时A^m=A^l成立,称A为本质(m,l)幂等矩阵.本文讨论了本质(m,l)幂等矩阵的特征.作为应用,给出了本质m对合、本质m幂等矩阵的等价刻画,讨论了最小多项式与本质(m,l)幂等矩阵的一些关系.

We call the matrix A as essential（m.l） idempotent matrix if there exists minimum natural numbers m such that A^m=A^l in which ml.This paper studies the character of essential（m,l） idempotent matrix.As application,it has given the equivalent characterizations of essential m involutory matrix and essential m idempotent matrix,and discussed the relationships between minimal polynomial and essential（m,l） idempotent matrix.