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Generalized Inverses: Real or Complex Field

In: Infinite Matrices and Their Recent Applications

Author

Listed:
  • P. N. Shivakumar

    (University of Manitoba, Department of Mathematics)

  • K. C. Sivakumar

    (Indian Institute of Technology, Madras, Department of Mathematics)

  • Yang Zhang

    (University of Manitoba, Department of Mathematics)

Abstract

The main objective of this chapter is to review certain recent results that were obtained in the context of generalized inverses of infinite matrices. These are presented in Sect. 4.2. We take this opportunity to review the basic ideas in the theory of generalized inverses of matrices and also operators acting between Hilbert spaces. This will be presented in the next section. We do not attempt at being exhaustive in our presentation. The intention is to give a brief idea of the notion of generalized inverses. Several excellent texts have been written on this topic. For matrices, for instance, we refer to the books by Ben-Israel and Greville [10], Meyer [73], and the classic text by Rao and Mitra [95]. For operators on general infinite dimensional spaces, see the book by Groetsch [41] and Nashed [77], where the latter includes extensive discussions on many algebraic as well as topological spaces. Let us note that in the next chapter, certain very new results on generalized inverses of matrices over quaternion polynomial rings are presented. For generalized inverses of matrices over commutative rings, an excellent source is the book by Bhaskara Rao [13].

Suggested Citation

  • P. N. Shivakumar & K. C. Sivakumar & Yang Zhang, 2016. "Generalized Inverses: Real or Complex Field," Springer Books, in: Infinite Matrices and Their Recent Applications, chapter 0, pages 41-48, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30180-8_4
    DOI: 10.1007/978-3-319-30180-8_4
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