(u,v)幂等矩阵与本质(m,l)幂等矩阵

(u,v)-idempotent matrices and essential(m,l)-idempotent matrices

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.

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 rootsεi.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.