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Homework Help: Linear Algebra - Bilinear Forms and Change of Basis

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the matrix of f relative to Alpha' and Beta'.

    Alpha' = [(1,0,0), (1,1,0), (2,-1,1)]
    Beta' = [(-13,9), (10,-7)]

    The question originally reads that f is a bilinear form.

    I've found a (correct according to answer key) matrix A that is

    3 -4
    4 -5
    -1 2

    from a given basis of
    Alpha = [(1,0,0), (1,1,0), (1,1,1)] and
    Beta = [(1,-1), (2,-1)]

    2. Relevant equations

    If Q is the matrix of transition from Alpha to basis Alpha' of U and P is the matrix of transition from Beta to basis Beta' of V, then QTAP = matrix of f relative to Alpha' and Beta'.
    T meaning transpose.

    3. The attempt at a solution
    I've gotten oh so far with this question, but I'm stuck here in the final part. I'm confused how to attain said matrices Q and P from the relevant equations. If I'm not terrible mistaken, I think I have to do something involving inverses but I'm at a loss here.

    Any help will of course be greatly appreciated.
  2. jcsd
  3. Mar 17, 2010 #2


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    You want to express the vectors of one basis in terms of the other basis.
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