对角线元为幂等矩阵的2×2分块方阵的数量幂等性

Scalar-idempotent Properties of 2×2 Square Matrix of All Diagonal Elements in the Set of Idempotent Matrices

设G是对角线元为幂等矩阵的2×2分块方阵,利用矩阵理论和方法,研究并得到了对角线元为幂等矩阵的2×2分块方阵G的k次数量幂等性,确定了方程Gk=λG有解的充要条件,其中k=2,3.

Let G be the 2×2 square matrix whose diagonal elements are idempotent matrices. By the matrix theory and methods, the k scalar - idempotent properties of the matrix G were studied, and the necessary and sufficient conditions for the existence of solution of equations G^k = A G were obtained . where k = 2.3.