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Math Help - index notation

  1. #1
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    index notation

    If I have a vector w and index it with, say, j then if w appears in another term in the equation do I use the same index i.e. j? Thanks
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  2. #2
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    Re: index notation

    An example would be helpful. Usually w_j is considered a function that maps a natural number j into the jth component of w (or maps a sequence of vectors w into the jth vector, depending on the meaning of "index w with j"). Then, as in any function, the argument can be anything, e.g., 0, j + 1, w_{i}, etc. But if you make a convention (even implicitly) that j ranges over vector indices, it is better to keep using j for this and not change it to, say, i without reason.
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  3. #3
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    Re: index notation

    ok I will try to prove (a x b) x (a x c)=a(a.(b x c)) using index notation. Can you give me latex for denoting a basis vector ( I mean a hat), and the delta,levi civita symbols please. Thanks
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  4. #4
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    Re: index notation

    [TEX]\hat{a}[/TEX] gives \hat{a}
    [TEX]\delta_{ijk}[/TEX] gives \delta_{ijk}
    [TEX]a\times b[/TEX] gives a\times b
    [TEX]a\cdot b[/TEX] gives a\cdot b.
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  5. #5
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    Re: index notation

    Thank you.

    (a\times b)/times(a\times c)
    = (\epsilon_{ijk}a_{i}b_{j}\hat{e_k}) x (epsilon_{ilm}a_{i}c_{l}\hat{e_m})
    = ( \delta_{jl}\delta_{km}- \delta_{jm}\delta_{lk})\epsilon_{kmn}\hat{e_n}a_{i  }a_{i}b_{j}c_{l}

    I appear to have gone wrong
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