The expression of the generalized Bott–Duffin inverse and its perturbation theory

摘要

Let L be a subspace of Cn and PL be the orthogonal projection of Cn onto L. Then for the n×n matrix A, the generalized Bott–Duffin (B–D) inverse A(L)(+) is given by A(L)(+)=PL(APL+I−PL)+. In this paper we will give an expression of A(L)(+). In the rest of the part, the perturbation analysis of A(L)(+) and the least squares solution of the generalized B–D equation Ax+y=b for x∈L and y∈L⊥ will be established under certain small perturbation of PLAPL.