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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

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    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!
     
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