Talk:Levi-Civita symbol

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This article incorporates material from PlanetMath, which is licensed under the GFDL.

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[edit] Examples

Could someone please explain the examples more clearly. Phrases like "it is obvious that.." or "it is clear that..." are hot very helpful, as it is all relative. Could someone please outline the steps for example 2 (and others if necessary) clearly, to be like an example is meant to be.

[edit] Levi-Civita (person)

Was Levi-Civita really a physician? I see nothing on that on his biographical article.Commander Nemet 05:25, 15 March 2006 (UTC)

Clearly this person means physicist. I have altered the article appropriately.Roonilwazlib 19:07, 22 May 2006 (UTC)

" It is actually a pseudotensor because under an orthogonal transformation of jacobian determinant −1 (i.e., a rotation composed with a reflection), it gets a -1." - It gets a -1? Could someone clarify this, maybe writing it explicitly with symbols? I don't get it. I'm trying to find out how the Levi-Civita symbol transforms and this hasn't helped... 203.97.255.167 22:01, 24 June 2006 (UTC)

Levi Civita is a HOLOR not a TENSOR, it does not transform like tensors do. Seeing as Wikipedia has no articles on Holor theory this may get confusing. Also the index conventions on this page are all wrong "superscipts should be considered equivalent with subscripts". Wrong.

[edit] Visualization matrix for εijk

I think the image showing the visualization of the symbol is not correct. If i corresponds to row, j corresponds to column, and k corresponds to the plane, then one should have the following representation:

first plane:

     0     0     0
     0     0     1
     0    -1     0

second plane:

     0     0    -1
     0     0     0
     1     0     0

third plane:

     0     1     0
    -1     0     0
     0     0     0

I may be wrong if i,j and k correspond to different directions than the one I mentioned above. Please correct. -- Myth (Talk) 14:17, 18 March 2007 (UTC)

I second this. They are obviously wrong, as the formulaic representation within the text states: e123=1 while the picture shows a -1. I also get the solution given above. How can the image be changed? -- User:xmaster1123 —Preceding comment was added at 08:58, 6 November 2007 (UTC)

[edit] Of course the sum is n!

The article asserts that it can be shown that (in n dimensions) the sum of the symbol as all its indices vary from 1 to n is n! Well, yeah! The symbol is nonzero precisely when its square is 1, which is precisely when the indices are a permutation of [n]. So the sum is exactly a count of the permutations of an n-set. And how many permutations exist? Why n! of them. QED.

My point is that the claim that "it can be shown..." strikes me as rather modest, since the proof is nearly self-evident. Anybody disagree?—PaulTanenbaum (talk) 03:48, 15 January 2008 (UTC)

[edit] error

There is a conflict between the 2 different places where the formula for the product of two LC symbols with 3 indices with 1 contracted appear. —Preceding unsigned comment added by 74.79.30.13 (talk) 22:44, 17 February 2008 (UTC)

[edit] Other notation for the three dimensional Levi-Civita symbol without case differentiation

\varepsilon _{ijk}=\frac{\left( j-i \right)\left( k-j \right)\left( k-i \right)}{2}

--77.125.156.157 (talk) 13:46, 28 May 2008 (UTC)