Perturbation analysis of the generalized Bott-Duff in inverse of L-zero matrices

Let L be a subspace of R-n and P-L be the orthogonal projection of R-n onto L. Then for the n x n matrix A, the generalized Bott-Duffin (B-D) inverse A((L))((+)) is given A((L))((+))=P-L(AP(L)+I-P-L)(+). In this article we prove that A((L))((+))=(P(L)AP(L))+ iff ALboolean ANDL(perpendicular to)=0. This result extends the concept so-called the "L-s.p.d" matrix proposed by Chen in his article "The Generalized Bott-Duffin Inverse and its Applications". In the rest part of the article, the perturbation analysis of A((L))((+)) and the least squares solution of the systems Ax+B*y=b, Bx=d are established under certain small perturbation of A.