矩阵的Γ逆在一类约束系统中的应用

An Application of T-inverses of Matrices to a Class of Constrained System

中文关键词:  矩阵的Γ逆  约束系统。

中文摘要:

      将矩阵的Γ逆应用于约束系统Ａｘ＋ｙ＝ｂ，ｘ∈Ｌ，ｙ∈Ｌ^⊥，对任意的Ａ和Ｌ，表示了它的一般解。当ＡＰ_Ｌ＋Ｐ_Ｌ⊥可逆时，这个解正是Ｂｏｔｔ—Ｄｕｆｆｉｎ解。并就Ｌ是Ａ的约化子空间、不变子空间及一般情形，讨论了相应的Γ逆存在的条件。

英文摘要:

      In this paper, we apply the Γ-inverses of matrices to the constrained system Ax + y=b,x ∈ L,g ∈ L^⊥, and express its general solution for arbitrary A and L。if AP_Ｌ+P_Ｌ⊥ arenonsingular,this solution is just Bott-Duffin solution。 The conditions for corresponding Γ-inverses exist are discussed for L to be a reducing or an invariant subspace。