IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-0622-0_9.html
   My bibliography  Save this book chapter

Quaternion Matrices

In: Real Quaternionic Calculus Handbook

Author

Listed:
  • João Pedro Morais

    (University of Aveiro, CIDMA)

  • Svetlin Georgiev

    (University of Sofia St Kliment Ohridski Faculty of Mathematics and Informatics, Department of Differential Equations)

  • Wolfgang Sprößig

    (TU Bergakademie Freiberg, Institut für Angewandte Analysis)

Abstract

In a brief outline, the next portion of text describes a way of representing quaternion matrices in such a way that quaternionic addition and multiplication correspond to matrix addition, (scalar) matrix multiplication, and matrix transposition. Besides the discussion of the quaternionic analogues to complex matrices, we will also discuss the possibility of decomposing quaternions with respect to well known matrix decompositions, which are related to solving systems of linear equations. Even though it is self-contained, the reader will comprehend the necessity of this notions while pursuing the subject. Our presentation is organized in such a way that the analogies between quaternion, noncommutativity, and quaternion matrix, on one hand, and determinant, rank, and eigenvalues, on the other, are mastered. The relations between these concepts will come into view more clearly through the text, motivating our insight to the problem.

Suggested Citation

  • João Pedro Morais & Svetlin Georgiev & Wolfgang Sprößig, 2014. "Quaternion Matrices," Springer Books, in: Real Quaternionic Calculus Handbook, edition 127, chapter 9, pages 133-147, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0622-0_9
    DOI: 10.1007/978-3-0348-0622-0_9
    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:978-3-0348-0622-0_9. 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.