The block independence in the generalized inverse AT,S(2) for some ordered matrices and applications

Guang-Jing Song and Shaowen Yu

Applied Mathematics and Computation, 2014, vol. 232, issue C, 399-410

Abstract: In this paper, the definition of block independence in the generalized inverse AT,S(2) is firstly given, and then a necessary and sufficient condition for some ordered matrices to be block independent in the generalized inverse AT,S(2) is derived. As an application, a necessary and sufficient condition forA1+A2+⋯+AkT,S(2)=A1T1,S1(2)+A2T2,S2(2)+⋯+AkTk,Sk(2)is proved. Moreover, some results are shown with respect to the Moore–Penrose inverse, the Weighted Moore–Penrose inverse and the Drazin inverse, respectively.

Keywords: Rank; Linear matrix expression; Moore–Penrose inverse; Drazin inverse; Weighted Moore–Penrose inverse; Block matrix (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:399-410

DOI: 10.1016/j.amc.2013.12.173

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