Introduction to vector spaces

[Ahmad Kishki]

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

 

[Fredrik]

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.

 

[Ahmad Kishki]

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?

 

[Fredrik]

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.

 

[verty]

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