- #1

quietrain

- 655

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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 (d

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 b

4)

and subsequently getting b

= [b(a.c)]

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 (d

_{mj}d_{nk}-d_{mk}d_{nj})a_{n}b_{j}c_{k}it becomes b_{m}a_{k}c_{k}-c_{m}a_{j}b_{j}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 b

_{m}a_{k}c_{k}, why doesn't it become b_{m}a_{n}c_{n}- ...4)

and subsequently getting b

_{m}a_{k}c_{k}-c_{m}a_{j}b_{j}= [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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