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Thread: 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 $\displaystyle w_j$ is considered a function that maps a natural number $\displaystyle j$ into the $\displaystyle j$th component of $\displaystyle w$ (or maps a sequence of vectors $\displaystyle w$ into the $\displaystyle j$th vector, depending on the meaning of "index $\displaystyle w$ with $\displaystyle j$"). Then, as in any function, the argument can be anything, e.g., 0, $\displaystyle j + 1$, $\displaystyle w_{i}$, etc. But if you make a convention (even implicitly) that $\displaystyle j$ ranges over vector indices, it is better to keep using $\displaystyle j$ for this and not change it to, say, $\displaystyle i$ 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 $\displaystyle \hat{a}$
    [TEX]\delta_{ijk}[/TEX] gives $\displaystyle \delta_{ijk}$
    [TEX]a\times b[/TEX] gives $\displaystyle a\times b$
    [TEX]a\cdot b[/TEX] gives $\displaystyle a\cdot b$.
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  5. #5
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    Re: index notation

    Thank you.

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

    I appear to have gone wrong
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