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Math Help - Suffix Notation

  1. #1
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    Suffix Notation

    Hi I;m just learning suffix notation and the summation convention.

    Just to check my understanding can someone just check to see if I've done this right,

    Define a new sort of multiplication by

    (\bf{A} \bullet \bf{B})_{ij}=(\bf{A})_{ik}(\bf{B})_{jk}

    Using suffix notation show that bullet multiplication isn't associative
    I've done it like so

    ((\bf{A} \bullet \bf{B}) \bullet \bf{C})_{ij} = (\bf{A} \bullet \bf{B})_{ik}(\bf{C})_{jk}=(\bf{A})_{im}(\bf{B})_{k  m}(\bf{C})_{jk}

    (\bf{A} \bullet (\bf{B} \bullet \bf{C}))_{ij}=(\bf{A})_{ik}(\bf{B} \bullet \bf{C})_{jk}=(\bf{A})_{jk}(\bf{B})_{jm}(\bf{C})_{k  m}

    As the components aren't equal bullet multiplication isn't associative
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thelostchild View Post
    Hi I;m just learning suffix notation and the summation convention.

    Just to check my understanding can someone just check to see if I've done this right,



    I've done it like so

    ((\bf{A} \bullet \bf{B}) \bullet \bf{C})_{ij} = (\bf{A} \bullet \bf{B})_{ik}(\bf{C})_{jk}=(\bf{A})_{im}(\bf{B})_{k  m}(\bf{C})_{jk}

    (\bf{A} \bullet (\bf{B} \bullet \bf{C}))_{ij}=(\bf{A})_{ik}(\bf{B} \bullet \bf{C})_{jk}=(\bf{A})_{jk}(\bf{B})_{jm}(\bf{C})_{k  m}

    As the components aren't equal bullet multiplication isn't associative
    You haven't shown that they are different, just that the expressions are not the same. A single simplified example though should show that they are not identically equal (a single counter example proves that a purported identity does not hold).

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    You haven't shown that they are different, just that the expressions are not the same. A single simplified example though should show that they are not identically equal (a single counter example proves that a purported identity does not hold).

    CB
    Darn I am an idiot, cheers
    Last edited by mr fantastic; April 26th 2009 at 04:45 AM. Reason: m --> r
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