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Matrices and bases

  1. Feb 10, 2010 #1
    I'm having some trouble understanding basis and how they relate to transformation matrices.
    1. The problem statement, all variables and given/known data
    Let e_1,e_2,e_3,e_4 be a basis in a four dimensional vector space V. Suppose that the linear transformation F on V has the matrix representation:
    [1 0 2 1;-1 2 1 3;1 2 5 5;2 -2 1 -2] (Matlab-notation).
    Find F:s matrix representation in the basis f_1= e_1-2e_2+e_4 , f_2=3e_2-e_3-e_4, f_3=e_3+e_4, f_4=2e_4.

    2. Relevant equations

    3. The attempt at a solution
    I thought of using B^(-1)AB (B is the basis A the transformation matrix), but I can't invert our basis here. What should I do?
  2. jcsd
  3. Feb 10, 2010 #2
    The e's represent the usual euclidian base e1 = (1,0,0,0), e2=(0,1,0,0) etc...
  4. Feb 10, 2010 #3


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    That's what you want to do, but I think you're trying to invert the wrong matrix.
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