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Homework Help: Representation of vectors by basis is Unique

  1. Oct 29, 2008 #1
    1. The problem statement, all variables and given/known data


    Representation of vectors by any basis is unique.

    2. Relevant equations

    3. The attempt at a solution

    The minimal span set and the maximum linearly independent set gives a basis.
  2. jcsd
  3. Oct 29, 2008 #2


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    Homework Helper
    Gold Member

    Try expanding a vector w into a basis set {w_i} using two different sets of coefficients i.e.

    [itex]\vec{w}=\sum_i a_i \hat{w}_i[/itex] and [itex]\vec{w}=\sum_i b_i \hat{w}_i[/itex]

    Then just show that a_i=b_i for all i.
    Last edited: Oct 29, 2008
  4. Oct 29, 2008 #3


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    Science Advisor

    gabbagabbahey's notation, think about the fact that
    [itex]\sum_i (a_i- b_i)\hat{w}_i= 0[/itex] and use the fact that the vectors are independent.
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