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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

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

    Fredrik

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    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
    Th
    Thank you, but will these recommendations be easy as self study?
     
  5. Jan 31, 2015 #4

    Fredrik

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    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

    verty

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    You could try Shilov's two books: Linear Algebra and Elementary Functional Analysis. The transition would be very smooth indeed.
     
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