Introduction to vector spaces

  • Linear Algebra
  • Thread starter Ahmad Kishki
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  • #1
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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
 
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  • #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.
 
  • #3
159
13
Th
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.
Thank you, but will these recommendations be easy as self study?
 
  • #4
Fredrik
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Thank you, but will these recommendations be easy as self study?
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.
 
  • #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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