IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v406y2021ics0096300321003763.html
   My bibliography  Save this article

Representations and symbolic computation of generalized inverses over fields

Author

Listed:
  • Stanimirović, Predrag S.
  • Ćirić, Miroslav
  • Lastra, Alberto
  • Sendra, Juan Rafael
  • Sendra, Juana

Abstract

This paper investigates representations of outer matrix inverses with prescribed range and/or null space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or null space and with meromorphic functional entries.

Suggested Citation

  • Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    • Handle: RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003763
    DOI: 10.1016/j.amc.2021.126287
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321003763
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126287?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Predrag S. Stanimirović & Miroslav Ćirić & Igor Stojanović & Dimitrios Gerontitis, 2017. "Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses," Complexity, Hindawi, vol. 2017, pages 1-27, June.
    2. Sendra, J. Rafael & Sendra, Juana, 2017. "Computation of Moore–Penrose generalized inverses of matrices with meromorphic function entries," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 355-366.
    3. Sendra, Juana & Rafael Sendra, J., 2015. "Gröbner basis computation of Drazin inverses with multivariate rational function entries," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 450-459.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dijana Mosić & Predrag S. Stanimirović & Spyridon D. Mourtas, 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    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. Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    4. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    5. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Sendra, J. Rafael & Sendra, Juana, 2017. "Computation of Moore–Penrose generalized inverses of matrices with meromorphic function entries," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 355-366.
    3. Beltrametti, M.C. & Sendra, J.R. & Sendra, J. & Torrente, M., 2020. "Moore–Penrose approach in the Hough transform framework," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    4. Kansal, Munish & Kumar, Sanjeev & Kaur, Manpreet, 2022. "An efficient matrix iteration family for finding the generalized outer inverse," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
    7. Haifa Bin Jebreen, 2019. "Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme," Mathematics, MDPI, vol. 7(8), pages 1-11, August.
    8. Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    9. Dijana Mosić & Predrag S. Stanimirović & Spyridon D. Mourtas, 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    10. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003763. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.