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Subclasses of generalized inverses of matrices

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Summary

Structure of allg-inverses of a matrix in a weak sense is shown. Characterizations of main subclasses ofg-inverses are investigated thoroughly. The dualities among subclasses and the relation betweeng-inverses and projections are stressed. The Gauss-Markov theorem reduces to a duality of two types ofg-inverses

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Authors and Affiliations

  1. Scientific Center, I.B.M. Japan, Japan

    Masaaki Sibuya

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  1. Masaaki Sibuya
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Additional information

A preliminary Japanese version was published by the author in theProc. Inst. Statist. Math., Vol. 17, (1969) with the title “Generalized inverses of matrices—Part 1”.

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Sibuya, M. Subclasses of generalized inverses of matrices. Ann Inst Stat Math 22, 543–556 (1970). https://doi.org/10.1007/BF02506375

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  • DOI: https://doi.org/10.1007/BF02506375

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