Condition number related to the outer inverse of a complex matrix

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Abstract

In this paper we obtain the formula for computing the condition number of a complex matrix, which is related to the outer generalized inverse of a given matrix. We use the Schur decomposition of a matrix. We characterize the spectral norm and the Frobenius norm of the relative condition number of the generalized inverse, and the level-2 condition number of the generalized inverse. The sensitivity for the generalized Drazin-inverse solution of linear systems is presented. We also present the structured perturbation of the generalized inverse. © 2009 Elsevier Inc. All rights reserved.

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Mosić, D., & Djordjević, D. S. (2009). Condition number related to the outer inverse of a complex matrix. Applied Mathematics and Computation, 215(8), 2826–2834. https://doi.org/10.1016/j.amc.2009.09.023

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