实数域上对角线元为幂等矩阵的2×2分块数量幂等矩阵的广义逆

The Generalized Inverses of 2×2 Scalar-idempotent Square Matrix of All Diagonal Elements as Scalar-Idempotent Matrices over Real Number Field

设G是实数域瓗上对角线元为幂等矩阵的2×2分块方阵,利用矩阵理论,研究了这类矩阵G的数量幂等性以及满足数量幂等性条件G^2=λG(0≠λ∈R))的矩阵的广义逆.通过研究得到了数量幂等性G^2=λG成立的条件,确定了满足条件G^2=λG的分块方阵G的{1}-逆,{3}-逆,{1,3}-逆以及其表达式.

Let G be the 2 × 2 square matrix where diagonal elements are idempotent matrices over real number field R. Based on the matrix theory,the scalar-idempotent properties of the matrix G and the Generalized Inverses of the specific matrix G where G^2= λG（λ∈R and λ≠0） were studied. Furthermore,the conditions for the existence of solution of equations G^2= λG were obtained,and {1}-inverses,{3}-inverses and {1,3}-inverses of the block matrix G in accordance with G^2= λG were ascertained,and the expressions for these Generalized Inverses were given out as well.