%0 Journal Article
%T (u，v)幂等矩阵与本质(m，l)幂等矩阵<br>(u，v)-idempotent matrices and essential (m，l)-idempotent matrices
%A 林志兴
%A 杨忠鹏
%A 陈梅香
%A 陈智雄
%A 陈少琼
%J 福州大学学报(自然科学版)
%D 2015
%R 10.7631/issn.1000-2243.2015.03.0311
%X 证明了(u，v)幂等矩阵与本质(m，l)幂等矩阵的互相确定关系，由此给出了求(u，v)幂等矩阵的Jordan标准形的方法，这种方法不依赖通常的求Jordan标准形的算法，只涉及到矩阵方幂的秩和u－v次单位根εi所确定的矩阵秩最后得到以矩阵秩为基本工具的，判定(u1，v1)幂等矩阵与(u2，v2)幂等矩阵相似的充分必要条件.<br>It has been proved that (u，v)-idempotent matrices and essential (m，l)-idempotent matrices can be determined by each other. Then it gives us a method to work out the Jordan canonical form of a (u，v)-idempotent matrix，independently on the usual method of the Jordan canonical form，only referring to the ranks of matrix powers and u-v-th unity roots εi . By using ranks of matrices as a basic tool，it also obtains some sufficient and necessary conditions for a (u1，v1)-idempotent matrix to be similar to a (u2，v2)-idempotent one
%K (u
%K v)幂等矩阵 本质(m
%K l)幂等矩阵 矩阵秩 Jordan标准形 矩阵相似&lt
%K br&gt
%K (u
%K v)-idempotent matrix essential (m
%K l)-idempotent matrix matrix rank Jordan canonical form matrix similar
%U http://xbzrb.fzu.edu.cn/ch/reader/view_abstract.aspx?file_no=201503004&flag=1