(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 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