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Determinantal Representations of the Core Inverse and Its Generalizations with Applications

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  • Ivan I. Kyrchei

Abstract

In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

Suggested Citation

  • Ivan I. Kyrchei, 2019. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications," Journal of Mathematics, Hindawi, vol. 2019, pages 1-13, October.
    • Handle: RePEc:hin:jjmath:1631979
    DOI: 10.1155/2019/1631979
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    Cited by:

    1. Ma, Haifeng & Stanimirović, Predrag S. & Mosić, Dijana & Kyrchei, Ivan I., 2021. "Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Stanimirović, Predrag S. & Mosić, Dijana & Wei, Yimin, 2022. "Generalizations of composite inverses with certain image and/or kernel," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    3. Mosić, Dijana & Zhang, Daochang & Stanimirović, Predrag S., 2024. "An extension of the MPD and MP weak group inverses," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    4. Mosić, Dijana & Stanimirović, Predrag S., 2022. "Expressions and properties of weak core inverse," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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