(m,/)秩幂等矩阵和(m,/)幂等矩阵的特性研究

On Characteristics of(m,l)Rank-idempotent Matrix and(m,l)Idempotent Matrix

如果存在自然数m，l（m〉l）使r（A^m）=r（A^l），称A为（m，l）秩幂等矩阵；当A^m=A^l时，称A为（m，l）幂等矩阵依据矩阵的幂等性与秩幂等性不随数域的改变而改变这一基本事实，应用Jordan标准形的性质，得到了这两类既有区别又有密切联系的矩阵类的特性刻画．

We call the matrix A as （m, l） rank-idempotent matrix if there exist natural numbers m, l（ m 〉 l） such that r（A^m） = r （A^l ） ; when A^m = A^l, then A is called （ m, 1 ） idempotent matrix. On the basis of the fact that idempotence and rank-idempotence of matrix are not changed with the number filed, applying the properties of the Jordan canonical form, this paper describes the characteristics of these two kinds of matrices which are different as well as close relationships.