Abstract: Let L be a subspace of Fⁿ and P_L be the orthogonal projection of Fⁿ onto L, where F=C or R. Let A be an n×n matrix. In this paper,we will give the perturbation analysis of the generalized Bott-Duffin inverse A_(L)⁽⁺⁾=P_L(AP_L+I-P_L)⁺ when A and L have small perturbation. Using this result, we establish a perturbation analysis to the least squares solution of the system Ax+ B*y=b, Bx=d under certain small perturbation of A and B.

Key words: L-zero matrix, perturbation analysis, orthogonal projection, generalized B-D inverse, L-zero matrix, perturbation analysis, orthogonal projection