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Thread: skew symmetric system problem

  1. #1 skew symmetric system problem 
    Forum Freshman Nabla's Avatar
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    The following system is skew symmetric in all of its indices:



    such that:



    I'm asked to prove it has 27 elements (easy since its ), and that 21 of these are zero. The remaining six occur when (p,r,s)=(1,2,3).

    How can I go about proving this? Thanks


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  3. #2 Re: skew symmetric system problem 
    . DrRocket's Avatar
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    Quote Originally Posted by Nabla
    The following system is skew symmetric in all of its indices:



    such that:



    I'm asked to prove it has 27 elements (easy since its ), and that 21 of these are zero. The remaining six occur when (p,r,s)=(1,2,3).

    How can I go about proving this? Thanks
    This sounds suspiciously like a homework problem.

    You need to do your own homework.

    It is actually pretty simple.


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  4. #3  
    Forum Freshman Nabla's Avatar
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    It's not homework, I'm working through some online notes on tensor calculus and differential geometry, as a personal task (I'm currently on my summer holidays). This is a question from the first section of those notes which introduces index notation.
    PHI is one 'H' of alot more interesting than PI!
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  5. #4  
    . DrRocket's Avatar
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    Quote Originally Posted by Nabla
    It's not homework, I'm working through some online notes on tensor calculus and differential geometry, as a personal task (I'm currently on my summer holidays). This is a question from the first section of those notes which introduces index notation.
    Then the result is very simple to prove. The skew symmetry implies that if you interchange any two indices then the result is the same as multiplying by -1, so if two indices are the same, then the term, being its own negative, must be 0. Therefore the only non-zero terms must be in cases in which the indices p,r,s take on different values and the ony available values are 1,2,3.
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  6. #5  
    Forum Freshman Nabla's Avatar
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    Thanks. That's actually really simple, I'm annoyed for not figuring it out myself.
    PHI is one 'H' of alot more interesting than PI!
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