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Math Help - Matrix proof - a question

  1. #1
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    Matrix proof - a question

    Can anyone tell me why the summation's upper bounds 4 and 3 are used in the attached proof? Thanks. I'm new to the forum, can't seem to get the equations to come out correctly, so I took a screen shot of them instead.
    Attached Thumbnails Attached Thumbnails Matrix proof - a question-capture.jpg  
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  2. #2
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    Re: Matrix proof - a question

    Quote Originally Posted by aerzo View Post
    Can anyone tell me why the summation's upper bounds 4 and 3 are used in the proof below? Thanks.

    Let A = [aij], B = [bij], C = [cij], AB = D = [dij], BC = E = [eij], (AB)C = F = [fij], and A(BC) = G = [gij]. To show that fij = gij for all i, j:

    [tex]
    4 4 3
    fij = Σ dikckj = Σ (Σ airbrk) ckj
    k=1 k=1 r=1
    and
    3 3 4
    gij = Σ airerj = Σ airbrkckj)
    r=1 r=1 k=1
    Please have a look at this thread

    Can you please make this more readable using LaTeX?
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  3. #3
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    Re: Matrix proof - a question

    Ok, I'm going to play with that, sorry for the confusing post.
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  4. #4
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    Re: Matrix proof - a question

    Quote Originally Posted by aerzo View Post
    Ok, I'm going to play with that, sorry for the confusing post.
    Somewhere in the instructions you must have been told the dimensions of those matrices.
    It seems some are 4\times 3 while others are 3\times 4.
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  5. #5
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    Re: Matrix proof - a question

    Quote Originally Posted by Plato View Post
    Somewhere in the instructions you must have been told the dimensions of those matrices.
    It seems some are 4\times 3 while others are 3\times 4.
    Thanks very much, sorry I didn't get around to fixing the text.
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