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Math Help - Notation question

  1. #1
    Senior Member Danneedshelp's Avatar
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    Notation question

    How are these different?


    AB=[c_{ij}]
    where c_{ij}=\sum_{k=1}a_{ik}b_{kj}

    and

    AB=[AB]_{ij}=\sum_{k=1}[A]_{ik}[b]_{kj}

    For instance,
    My book proves the distributive property of multiplication as follows (im going to leave stuff out)

    A(B+C)=a_{i1}(b_{1j}+c_{1j})+...+a_{in}(b_{in}+c_{  nj})

    Then you expand AB+AC and do some regrouping to find A(B+C)=AB+AC

    But, in another text I found the same proof done with the afore mentioned notation

    [A(B+C)]_{ij}=[A]_{*i}[(B+C)]_{*j}=\sum_{k}[A]_{ik}[B+C]_{kj}...

    I don't understand how to read the latter proof. What's being done in the proof makes sense to me, but I'm just not sure how to read the notation I guess.

    Last edited by Danneedshelp; June 30th 2009 at 03:42 PM.
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  2. #2
    Super Member malaygoel's Avatar
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    India
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    This might be of some help.

    [A]_{ij} represents (i,j) element of the matrix.

    [A]_{i*} represents i^{th} row of the matrix

    [A]_{*j} represents j^{th} column of the matrix

    <br />
[A(B+C)]_{ij}=[A]_{*i}[(B+C)]_{*j}=\sum_{k}[A]_{ik}[B+C]_{kj}...<br />
    it is [A]_{i*} in place of [A]_{*i}
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Essentially they are the same with [A]_{ij}=a_{ij}, and as malaygeol sort of said, [A]_{i*}=\sum_{k}a_{ik}.

    Also, [c_{ij}] is the entire matrix while [C]_{ij} is just one element of it, and also (I presume) the c such that AB=[c_{ij}] is different from the c such that C=[c_{ij}], if that makes sense...

    With notation problems like this I tend to just guess - if you understand what it is mean to be then you can often work out what the notation means. If it makes sense it is probably true.
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  4. #4
    Senior Member Danneedshelp's Avatar
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    Thank you both, everything makes sense now. You pretty much solidified what I thought. I just wasn’t 100% sure.

    Thanks
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