IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-30180-8_2.html
   My bibliography  Save this book chapter

Finite Matrices and Their Nonsingularity

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

Nonsingularity of matrices plays a vital role in the solution of linear systems, matrix computations, and numerical analysis. A large variety of problems arising in computational fluid mechanics, fluid dynamics, and material engineering that are modelled using difference equations or finite element methods require that the matrix under consideration is nonsingular, in order for the numerical schemes to be convergent. In spite of the large scale availability of excellent software for the computation of eigenvalues, there is always a growing need for new results on invertibility of matrices and inclusion regions of spectra of matrices. This is true especially due to the fact that in practical problems, matrices are dependent on parameters. Further, bounds for eigenvalues of finite matrices usually lead to derivation of bounds for the spectra of infinite matrices. Due to these reasons, discovering new sufficient conditions for matrix invertibility and eigenvalue inclusion regions are very relevant even today.

Suggested Citation

  • P. N. Shivakumar & K. C. Sivakumar & Yang Zhang, 2016. "Finite Matrices and Their Nonsingularity," Springer Books, in: Infinite Matrices and Their Recent Applications, chapter 0, pages 5-25, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30180-8_2
    DOI: 10.1007/978-3-319-30180-8_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-319-30180-8_2. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.