# Math Help - index notation

1. ## 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

2. ## Re: index notation

An example would be helpful. Usually $w_j$ is considered a function that maps a natural number $j$ into the $j$th component of $w$ (or maps a sequence of vectors $w$ into the $j$th 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.

3. ## 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

4. ## 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 $a\cdot b$.

5. ## 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