Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Concept of a basis for a vector space

  1. Dec 1, 2007 #1
    concept of a "basis" for a vector space

    I do not understand the concept of a "basis" for a vector space.

    Here's an example from my practice final exam:

    Suppose U and V are subspaces of the real vector space W and {u1} is a basis for U and {v1} is a basis for V. If U intersection V = {0} show that {u1, v1} is a linearly independent set it W.

    I probably need additional help with this example, but if someone could explain a "basis" to me in terms of this example I would greatly appreciate it.

    Thanks.
     
  2. jcsd
  3. Dec 1, 2007 #2

    EnumaElish

    User Avatar
    Science Advisor
    Homework Helper

    Any vector in U can be expressed as a linear transformation of u1 (e.g., k*u1). Any vector in V can be expressed as a linear transformation of v1 (e.g., k*v1).
     
  4. Dec 1, 2007 #3
    Ok, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Concept of a basis for a vector space
  1. Vector Space: Basis (Replies: 8)

  2. Basis of a vector space (Replies: 10)

  3. Vector Space Basis (Replies: 4)

  4. Vector space and basis (Replies: 9)

Loading...