Talk:Einstein notation
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The text I copied from tensor said: both raised and lowered on the same side. When I did Lagrangian mechanics, it was twice on the same side, which allow dot and cross products to be written in this way -- Tarquin 20:13 Mar 13, 2003 (UTC)
- In general, either are used but in several fields (i.e. spacetime geometry) the up/down is required and correspond to a 'tensor contraction'. -- looxix 20:36 Mar 13, 2003 (UTC)
Can we add this funny Einstein's comment stolen from Wolfram:
- The convention was introduced by Einstein (1916, sec. 5), who later jested to a friend, "I have made a great discovery in mathematics; I have suppressed the summation sign every time that the summation must be made over an index which occurs twice..." (Kollros 1956; Pais 1982, p. 216).
- -- looxix 00:14 Mar 14, 2003 (UTC)
Don't see why not -- Tarquin 11:40 Mar 14, 2003 (UTC)
http://mathworld.wolfram.com/EinsteinSummation.html
I will write the next section, but not until tomorrow at least. I may not be up to the last section, however. Both of these are briefly described in Appendix 3 of Wald's 1994 QFT in CS & BHT book. So you can look there if you want to write them! ^_^ -- Toby 07:16 Mar 18, 2003 (UTC)
IE6 does not show ⊗ (& otimes;) - Patrick 11:00 Mar 18, 2003 (UTC)
I try to explain in the surrounding context what the missing symbol would be when I do something like this. But there are alternatives short of going to full-blown texvc. Can you give some advice for your browser:
- V ⊗ W (relying on context to know what the box represents);
- V (x) W (long used by mathematicians in ASCII contexts like Usenet);
- V x W (relying on context to know what kind of multiplication is involved);
- V
W (a less distorted picture than that produced by texvc).
-- Toby 00:05 Mar 20, 2003 (UTC)
The box is not clear, the same one appears for every symbol that can not be represented. #3 and #4 both are fine. - Patrick 01:06 Mar 20, 2003 (UTC)
some details
The basic rule is:
v = vi ei.
In this expression, it is assumed that the term on the right side is to be summed as i goes from 1 to n, because the index i appears on both sides. In that case, the equation is indeed true.
I guess what is meant is "because the index i appears twice", or maybe "because the index i doesn't appear on both sides".
Here, the Levi-Civita symbol e (or ε) satisfies eijk is 1 if (i,j,k) is a positive permutation of (1,2,3), -1 if it's a negative permutation, and 0 if it's not a permutation of (1,2,3) at all.
Shouldn't it be odd and even permutations, rahter than positive and negative? (I don't know if the terms 'positive' and 'negative' are common use, but if it is the case then they should appear in the "permutations" page...)
Make more simple?
I think this article could be made simpler. For example, it would be greatly enhanced with the Riemman summation symbol at least once in the article (preferably in the definition), and a strategic use of the word "implicit". (preferably in the definition) Kevin Baas | talk 22:11, 2004 Jul 31 (UTC)