Perturbation Analysis of the Generalized Bott-Duffin Inverse ofL-zero Matrices
Guoliang Chen, Guoming Liu, Yifeng Xue · Linear and Multilinear Algebra · 2003
Let L be a subspace of ${\bf R}^n$ and P L be the orthogonal projection of R n onto L . Then for the n × 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 article we prove that $A^{(+)}_{(L)}=(P_LAP_L)^+$ iff $AL\cap L^\perp =0$ . 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 .