Talk:Einstein notation

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Mathematics

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"Name of matrix representation of a vector?"

In the subsection "Vector representations" of this article a vector is represented in two forms, a summation form and a matrix product form. Is there a source for this representation? What is the name of the matrix whose components are basis vectors? --GeraldMeyers (talk) 01:52, 28 May 2022 (UTC)[reply]

"Kronecker delta"

This formula makes something simple seem complex and very obscure:

\mathbf {e} ^{i}(\mathbf {e} _{j})=\delta _{j}^{i}.

I clicked on Kronecker delta, and it just means 1 if i=j and 0 otherwise! Could the page just state that rather than introducing yet another Greek letter and requiring the reader to open another page to understand what it means? — Preceding unsigned comment added by 71.82.237.223 (talk) 23:29, 17 November 2018 (UTC)[reply]

Mnemonics Section

This seems to be very misleading. Isn't it the case that the super-/ subscripts just don't correspond in any neat way to directions in matrices? Contraction merely requires that the contra and co indices have the same symbol. But contraction in matrix calculus depends on the order of the multiplication, no? —Preceding unsigned comment added by 75.16.138.214 (talk) 21:57, 21 January 2010 (UTC)[reply]

This section is probably not about matrices - but it's not very clear. The whole Vector representations section seems to be more about the covariance and contravariance of vectors than about Einstein's summation convention, and so perhaps is not very relevant. --catslash (talk) 15:15, 22 January 2010 (UTC)[reply]

There is a handy mnemonic not mentioned in the article. Contra-variants, super-scripts, and column vectors belong together since they all have 2 syllables. Co-variants, sub-scripts, and row vectors belong together since they all have 1 syllable. As far as I know, this is my own idea, though only a memory trick. CharlesTheBold (talk) 03:51, 12 February 2012 (UTC)[reply]

Formulae list at the end...

Where to put the section Einstein notation #Coefficients on tensors and related? That list of formulae is not necessary for understanding the summation convention, though certainly not to be deleted, so should be placed somewhere else... F = q(E+v×B) ⇄ ∑_ic_i 15:57, 11 April 2012 (UTC)[reply]

For now, I'd suggest moving it to Ricci calculus. It belongs there better than here, and fits with the "summary nature" of that article. This article still needs a lot of other trimming: it tries to deal with covariance and contravariance in far too much detail. All that is needed is enough to understand that when dealing with covariance and contravariance tracked by upper and lower indices, in the summation convention this results in summation being between one upper and one lower index. But this can be left for when someone feels this way inclined. — Quondum ^☏ 17:06, 11 April 2012 (UTC)[reply]

Ok - I also proposed so at wikiproject maths talk. It will be cut and pasted to Ricci calculus. F = q(E+v×B) ⇄ ∑_ic_i 18:54, 11 April 2012 (UTC)[reply]

More trimming

There may be some sentences you edited Quondum, that simply I intend to just remove (where it becomes unecessersarily intricate on linear algebra, but not just co/contra-variance, as you say). Feel free to revert/recover anything if you think so (or any editors which come here). F = q(E+v×B) ⇄ ∑_ic_i 19:10, 11 April 2012 (UTC)[reply]

Both indices as subscripts.

Some people (e.g. Cambridge university) subscript both indices. This should probably be mentioned. — Preceding unsigned comment added by 86.138.91.7 (talk) 19:01, 2 February 2013 (UTC)[reply]

See the archived discussion: Would be much clearer to do the Euclidean case first (no raised/lowered distinction). The consensus seems to have been yes, but there were no volunteers to do the work. --catslash (talk) 21:11, 2 February 2013 (UTC)[reply]

I disagree with first mentioning subscripts only (this being an attempt at a pedagogical approach), but agree that the case where only subscripts are used could be mentioned a little more in-depth, as it occurs commonly enough (this is glancingly mentioned in Einstein notation#Superscripts and subscripts vs. only subscripts). — Quondum 18:57, 3 February 2013 (UTC)[reply]

Reference?

Is it something similar to http://www.feynmanlectures.caltech.edu/II_25.html#Ch25-S2 ? — Preceding unsigned comment added by 148.81.172.134 (talk) 07:13, 3 October 2019 (UTC)[reply]

404 in Reference

Reference [1] ("The Foundation of the General Theory of Relativity") link to the original 404s — Preceding unsigned comment added by 108.162.75.221 (talk) 17:19, 14 May 2020 (UTC)[reply]

This "notation" introduces a lot of ambiguity

Rather than having index literals as superscript, all index literals should be subscript in order to prevent ambiguity.

upper and lower indices

I am confused on when to write uper and lower index:

In Einstein notation#Inner product we see ${\displaystyle \langle \mathbf {e} _{i},\mathbf {e} _{j}\rangle u^{i}v^{j}}$ . Here the scalar product of two basis vectors is ${\displaystyle \langle \mathbf {e} _{i},\mathbf {e} _{j}\rangle }$ (all lower index) while in Einstein notation#Abstract description it is ${\displaystyle \mathbf {e} ^{i}(\mathbf {e} _{j})}$ (mixed indices).

[[1]] does not help.

Did I overlook something in the text?

Jyyb (talk) 11:30, 6 December 2024 (UTC)[reply]