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

Let L be a subspace of C" and P-L be the orthogonal projection of C-n onto L. Then for the n x n matrix A, the generalized Bott-Duffin (B-D) inverse A((L))((+)) is given by A((L))((+)) = P-L(AP(L) + I - P-L)(+). 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 is an element of L and y E L-perpendicular to will be established under certain small perturbation of P(L)AP(L). (C) 2002 Elsevier Science Inc. All rights reserved.