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Math Help - linear algebra question

  1. #1
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    linear algebra question

    linear algebra question-screen-shot-2013-02-26-12.06.31-pm.png

    in the question why can you change the order of AB and BA in

    5(AB^T)^T = 5(B^T)^T A^T ?

    where ^T means the transpose of a matrix
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  2. #2
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    Re: linear algebra question

    This is a standard property of transposition ( (AB)^T=B^TA^T). Let A be an n\times m matrix and let B be an m\times n matrix. Now consider their transposes A^T and B^T. Row i of A is exactly the same as column i of A^T, similarly column i of B is exactly the same as row i of B^T. So you should be able to see that

    row_i(A)\cdot column_j(B)=row_j(B^T)\cdot column_i(A^T),

    so it follows that (AB)^T=B^TA^T.
    Last edited by hairymclairy; February 27th 2013 at 01:04 AM.
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