Startseite Two closed novel formulas for the generalized inverse A T,S (2) of a complex matrix with given rank
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Two closed novel formulas for the generalized inverse A T,S (2) of a complex matrix with given rank

  • Xingping Sheng ORCID logo EMAIL logo
Veröffentlicht/Copyright: 16. Juli 2019

Abstract

In this paper, two novel closed formulas for the generalized inverse A T , S ( 2 ) of a complex matrix A are established based on the expression A T , S ( 2 ) = G ( A G ) g = ( G A ) g G , according to the matrix G with given different ranks, where G is a matrix such that R ( G ) = T and N ( G ) = S . The two formula express each component of A T , S ( 2 ) as a rational function of the components of the matrices A and G, the efficiency of which is shown by some numerical examples.

MSC 2010: 65H05

Award Identifier / Grant number: 11771076

Award Identifier / Grant number: 1508085MA12

Award Identifier / Grant number: gxyqZD2016188

Funding statement: This project was supported by NSF China (No. 11771076), Natural Science Foundation of Anhui Province (No. 1508085MA12) and Key projects of Anhui Provincial University excellent talent support program (No. gxyqZD2016188).

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments and suggestions that improved the presentation of the paper.

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Received: 2018-03-28
Revised: 2019-04-22
Accepted: 2019-05-04
Published Online: 2019-07-16
Published in Print: 2020-02-01

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