1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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 Introduction to vector spaces

  1. Jan 31, 2015 #1
    i want a book that smoothly takes me from finite dimensional vector spaces to infinite dimensional vector spaces. Edit: I am doing this as self study, so i would prefer the book to be easy going without an instructor

    Last edited: Jan 31, 2015
  2. jcsd
  3. Jan 31, 2015 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Kreyszig (Introductory functional analysis with applications) is considered the easiest introduction to functional analysis. I haven't read it though.

    Conway (A course in functional analysis) is extremely hard to read (because he skips details and assumes that you're already very good at topology), but I think he does the stuff about orthonormal bases better than anyone else.
  4. Jan 31, 2015 #3
    Thank you, but will these recommendations be easy as self study?
  5. Jan 31, 2015 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Kreyszig: Maybe. This is supposed to be the easiest book, but it's a difficult topic, so even the easiest book may be difficult.

    Conway: Definitely not. You would need to spend at least a couple of months studying topology before you give this book a shot. If you know just a little topology however, you can try to take a look at the stuff on orthonormal bases. It's easier than the rest of the book.
  6. Feb 3, 2015 #5


    User Avatar
    Homework Helper

    You could try Shilov's two books: Linear Algebra and Elementary Functional Analysis. The transition would be very smooth indeed.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Introduction vector spaces Date
Introduction to Conformal Field Jun 24, 2017
Prob/Stats Textbook of "introduction to mathematical thinking" Apr 29, 2017
Quantum Introduction to scattering Dec 30, 2016
Topology Introduction to Topological Manifolds by John Lee (prereqs) Dec 25, 2016