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Math Help - The General Idea of Vector Spaces?

  1. #1
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    The General Idea of Vector Spaces?

    Hi everyone,

    I got through my linear algebra class (PHEW!) but I have kind of an in general question that I hope some of you can shed some light on.

    The textbook we used focused mainly on vectors in R ^n. It really didn't address the generality of vector spaces until the very end, and we discussed it for MAYBE a day and a half, if that. Can anyone shed any light on exactly what a vector space is ? I feel like that is the crux of this course, and I haven't quite grasped the concept of a vector space.

    Any comments are extremely appreciated. If this is too "in general", please let me know and I will try to narrow my focus to specific questions.

    Thanks for reading, I hope to get some replies!
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    Quote Originally Posted by elizsimca View Post
    The textbook we used focused mainly on vectors in R ^n. It really didn't address the generality of vector spaces until the very end, and we discussed it for MAYBE a day and a half, if that. Can anyone shed any light on exactly what a vector space is ? I feel like that is the crux of this course, and I haven't quite grasped the concept of a vector space.
    Linear algebra is the study of vector spaces. In an elementary (undergraduate) linear algebra course the course is not made abstract because it is assumed that this abstraction will confuse many students. Rather, the course concentrates mostly on the vector space \mathbb{R}^n because it is easier to visualize. I cannot think of any easy way to explain what a vector space is, one that you would find in a popular mathematics book, I can give an abstract definition but that would not make much sense and you probably seen it already. Basically a vector space is trying to generalize the same properties you find in \mathbb{R}^n: like a basis, linear independence, ... and so on.
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