Condition numbers for the outer inverse and constrained singular linear system q Huaian Diao a , Mei Qin b , Yimin Wei c, * a Department of Mathematics, City University of Hong Kong, Hong Kong, PR China b Institute of Mathematics, Fudan University, Shanghai 200433, PR China c Department of Mathematics, Fudan University, Shanghai 200433, PR China Abstract In this paper, we investigate the condition number of the outer inverse A ð2Þ T ;S and outer inverse A ð2Þ T ;S solution of constrained linear system Ax = b, x 2 T, where A is a real m · n matrix, b and x are real vectors, T is a subspace. Let a and b be two positive real num- bers, when we consider the weighted Frobenius norm k½aA; bbk ðFÞ QP on the data we get the formula of condition number for the outer inverse A ð2Þ T ;S solution of constrained linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated. Ó 2005 Elsevier Inc. All rights reserved. Keywords: The outer inverse A ð2Þ T ;S ; The outer inverse A ð2Þ T ;S solution; Constrained linear system; Condition number; Componentwise perturbation; Sensitivity 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.04.099 q This project is supported by the National Natural Science Foundation of China under grant 10471027 and Shanghai Education Commission. * Corresponding author. E-mail addresses: hadiao78@yahoo.com (H. Diao), qinmay2002@yahoo.com.cn (M. Qin), ymwei@fudan.edu.cn (Y. Wei). Applied Mathematics and Computation 174 (2006) 588–612 www.elsevier.com/locate/amc