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Math Help - Transposing Matrices

  1. #1
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    Transposing Matrices

    Hi, i'm struggling with this question and really need a push in the right direction... i haven't the faintest idea of what to do here... we haven't learnt about transposing maxtrices yet, I just saw something about it in a text book so I have a vague idea, but I don't really know how to go about proving this:

    If A is an m x n matrix with (i,j)- entry a_{ij}, let A^{\dagger} be the n x m matrix with (i,j)- entry a_{ji}. Show that if the product C= AB is defined, then so is B^{\dagger}A^{\dagger}, and that B^{\dagger}A^{\dagger} = C^{\dagger} .

    I'd really appreciate any help you guys could give me, cheers.

    thanks in advance!

    rorosingsong
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  2. #2
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    I think you need to apply the properties of matrix tranposition

    If C = AB then C' = (AB)' = A'B'

    More here

    Transpose - Wikipedia, the free encyclopedia
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  3. #3
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    Thanks pickslides! Appreciate it. =)
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  4. #4
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    Quote Originally Posted by pickslides View Post
    I think you need to apply the properties of matrix tranposition

    If C = AB then C' = (AB)' = A'B'

    More here

    Transpose - Wikipedia, the free encyclopedia
    Except that \displaystyle (\mathbf{AB})^T \neq \mathbf{A}^T\mathbf{B}^T.

    However, \displaystyle (\mathbf{AB})^T = \mathbf{B}^T\mathbf{A}^T.
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