IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-14794-9_2.html
   My bibliography  Save this book chapter

Vector Spaces

In: An Introduction to Tensors and Group Theory for Physicists

Author

Listed:
  • Nadir Jeevanjee

    (University of California at Berkeley, Department of Physics)

Abstract

This chapter reviews the basic linear algebra essential for understanding tensors (linear independence, bases, linear operators, etc.), and also develops some more advanced linear algebraic notions (e.g., dual spaces and non-degenerate Hermitian forms) which are also essential but often undiscussed. This chapter also takes a more abstract point of view than is typical, which gives us the freedom to consider vector spaces made up of functions or matrices, rather than just vectors in Euclidean space. Throughout, special care is taken to distinguish the component representation of various objects (vectors, linear operators, etc.) from their existence as coordinate-free abstract objects. The machinery developed is also used to illuminate enigmatic topics such as spherical harmonics and the relationship between bras and kets and the covariant and contravariant components of a vector.

Suggested Citation

  • Nadir Jeevanjee, 2015. "Vector Spaces," Springer Books, in: An Introduction to Tensors and Group Theory for Physicists, edition 2, chapter 0, pages 11-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-14794-9_2
    DOI: 10.1007/978-3-319-14794-9_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

    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:978-3-319-14794-9_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.