- #1
quietrain
- 655
- 2
hi, i don't understand why levi civita symbols is equal to kronecker delta when i was reading the wikipedia on it http://en.wikipedia.org/wiki/Levi-Civita_symbol
namely,
1)why does EijkElmn = det [ 9 terms of kronecker delta]
how do we know its those 9 terms? like dil dim din etc
2)and since they use det, does it mean EijkElmn is a cross product?
also from this link http://folk.uio.no/patricg/teaching/a112/levi-civita/
on the proof of the vector triple product,
3)why from (dmj dnk-dmk dnj)an bj ck it becomes bm ak ck-cm aj bj
i understand that the kronecker delta is something like a dirac delta function, which acts like a "sifting function" but if there are 2 kronecker delta, then how does it work?
so example instead of bm ak ck, why doesn't it become bmancn - ...
4)
and subsequently getting bm ak ck-cm aj bj
= [b(a.c)]m - [c(a.b)]m
what does the subscript m stands for? and how did they get to the bac-cab expression? if the j and k subscripts means dot products, then what are the other 2 components of the dot product? it has so many alphabets><
does it has anyhting to do with dummy index and free index?
also, from
is it right to think that the subscript i is the x-plane in cartesian form?
so if i want the z-plane, then would it mean to use the k component? so in this equations, is the k used here equal to the k in cartesian? if it is the same, then how do i get the k-component since they will clash?
5)also what does the subscript i means? component?
if i just want to have the triple product alone without the component i, what will it be?
thanks!
namely,
1)why does EijkElmn = det [ 9 terms of kronecker delta]
how do we know its those 9 terms? like dil dim din etc
2)and since they use det, does it mean EijkElmn is a cross product?
also from this link http://folk.uio.no/patricg/teaching/a112/levi-civita/
on the proof of the vector triple product,
3)why from (dmj dnk-dmk dnj)an bj ck it becomes bm ak ck-cm aj bj
i understand that the kronecker delta is something like a dirac delta function, which acts like a "sifting function" but if there are 2 kronecker delta, then how does it work?
so example instead of bm ak ck, why doesn't it become bmancn - ...
4)
and subsequently getting bm ak ck-cm aj bj
= [b(a.c)]m - [c(a.b)]m
what does the subscript m stands for? and how did they get to the bac-cab expression? if the j and k subscripts means dot products, then what are the other 2 components of the dot product? it has so many alphabets><
does it has anyhting to do with dummy index and free index?
also, from
is it right to think that the subscript i is the x-plane in cartesian form?
so if i want the z-plane, then would it mean to use the k component? so in this equations, is the k used here equal to the k in cartesian? if it is the same, then how do i get the k-component since they will clash?
5)also what does the subscript i means? component?
if i just want to have the triple product alone without the component i, what will it be?
thanks!
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