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Math Help - Change of Basis- Please help

  1. #1
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    Change of Basis- Please help



    Please help me, i just dont get change of basis. The book omits the steps and i dont understand the notation to understand what exactly i am supposed to do.


    This is the example in the book, i dont understand how they arrive at the solution because i dont understand what the notation means and it is driving me insane already because i am sure that the actual calculations are easy.


    x1+x2+x3=0 is a plane, consider the bases U and B in this plane.

    U= (a1,a2)= (0,1,-1), (1,0,-1)
    B= (b1,b2) = ( 1,2,-3),(4,-1,-3)


    Find the change of basis matrix.

    The book then does

    [b1]subscript U= [2,1]





    Also if I have diagnolized a matrix how do i find the change of basis matrix to go from the original to the diagnol?
    Last edited by mr fantastic; May 18th 2009 at 03:49 AM. Reason: Deleted excessive smilies.
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  2. #2
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    Quote Originally Posted by SydneyBristow View Post
    U= (a1,a2)= (0,1,-1), (1,0,-1)
    B= (b1,b2) = ( 1,2,-3),(4,-1,-3)

    Find the change of basis matrix.

    The book then does

    [b1]subscript U= [2,1]
    What they mean by {b_1}_U is likely b_1 relative to the U basis.

    I.e. b_1 = 2a_1 + 1a_2 = (2,1) relative to U.

    Remember, U and B are both bases for the same subspace of \mathbb{R}^3, so any vector in B can be expressed as a linear combination of the vectors in U, and vice versa. In doing so, you get its co-ordinates relative to that basis.
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