Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra and QM

  1. Mar 13, 2010 #1
    is there a reference book in linar algebra that covers topics found in studying quantum mechanics like: vector spaces, operators , matrix , eigenvectors and eigenvalues.
    i mean not a physics book, i want a mathematics book that talks about these notions and others in an abstarct way (not dedicated to quantum mechanics)

    thank you
  2. jcsd
  3. Mar 13, 2010 #2
    Last edited by a moderator: May 4, 2017
  4. Mar 13, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Any book on linear algebra will do. My favorite is Axler.

    Note that linear algebra is the mathematics of linear operators between finite-dimensional vector spaces, but we often have to deal with infinite-dimensional vector spaces in QM. The mathematics of linear operators between infinite-dimensional vector spaces is called functional analysis, but you can understand QM very well without ever opening up a book on functional analysis, because linear algebra will give you the right intuition about things. (A lot of results about finite-dimensional vector spaces hold for infinite-dimensional ones too, but the proofs are often much, much harder). If you want to check out a book on functional analysis, Kreyszig is probably the best choice. I haven't read it myself, but it's getting very good reviews.
  5. Mar 13, 2010 #4
    thank you,
    but isnt there a book that talk about vector spaces in an abstract manner like the mathematicians do?
  6. Mar 13, 2010 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Any book on linear algebra or functional analysis meets that requirement. (In particular the ones I recommended).

    Edit: I realize now that you were answering Qubix, not me.
  7. Mar 13, 2010 #6
    Take a look at
    Bernard Friedman, "Principles and Techniques of Applied
    Mathematics" (John Wiley and Sons, New York, 1956).
    Don't let its age keep you away from it. The math has not changed in 50 years. It is still a great book today.
  8. Mar 15, 2010 #7
    yes i mean Qubix.
    thank you for your explanation about algebra of finit and infinit dimensional spaces.

    and the book of axler:Linear algebra done right is a great book. thank you.:smile:

    thank you, but that book is not dedicated to linear algebra, perhaps the first two chapters are about linar algebra.
  9. Mar 19, 2010 #8
    i have that great book in hands, and i am reading it, it covers most of the linear algebra found in quantum mechanics,and it treats linar algebra in abstract way, it has exercises with solutions (separate solutions manual). good book.
  10. Mar 19, 2010 #9
    You could also look at Paul Halmos: "Finite Dimensional Vector Spaces". He had in mind when writing it proofs that would generalise readily to the infinite dimensional case whenever possible (and has also written a dedicated book on Hilbert Space).
  11. Mar 20, 2010 #10
    Sheldon Axler - Linear Algebra done Right

    or, if you really want to learn algebra the mathematician's way

    Serge Lang - Algebra (but it's pretty difficult and deep, most of it is useless for quantum mechanics)
  12. Mar 20, 2010 #11
    Serge Lang's 'Algebra' made me cry, wet the bed, and forget the FOIL method before my head just burst like a tick. I wouldn't wish that tome a physicist if they smacked me! :rofl:
  13. Mar 20, 2010 #12
    If you seriously want the underlying maths you will need Affine spaces as well as linear ones.

    Tensor Geometry: The geometric viewpoint and its uses

    by C T J Dodson and T Poston

    is the ideal book.
  14. Mar 20, 2010 #13
    yes , it is a great book too, i had found it in references section of a "quantum computation and information" book.

    and i thank all of you who had contributed to this thread. your informations and suggestions are great.:smile:
  15. Mar 20, 2010 #14
    Yup, nothing like a really hot reading list to get the blood pumping right?! :smile:
  16. Mar 20, 2010 #15
    yes, it is an advanced book,
    Serge Lang has other books about linear algebra such as:"Linear algebra" and "introduction to linear algebra"
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook