Talk:Covariant transformation

message: At first glance this article is better. —Ben FrantzDale 23:51, 30 August 2006 (UTC)
replies: text: There are at least three related articles that are closely related and need cleanup: this one, covariance and contravariance, and differential form. Thoughts? —Ben FrantzDale 10:12, 11 May 2007 (UTC)
replies: text: Leave differential form out of it. It is another example of pointless abstraction, like category theory. JRSpriggs 11:06, 11 May 2007 (UTC)
replies: text: I also support merging of this one and covariance and contravariance. Both articles have their merits and demerits and a merged article will contribute toward completeness and clarity which is lacking in many points. Lantonov 14:32, 23 July 2007 (UTC)
replies: text: Covariance, contravariance and the associated transformations cannot reasonably discussed without fully discussing the others. In consequence, the content of the articles are to all intents duplicated. The topic is however more general, hence a merge of the articles Covariant transformation and Covariance and contravariance of vectors to a broader article Covariance and contravariance of tensors (currently a redirect) should be considered, in which vectors should be discussed en route to the complete concept. — Quondum☏ 12:20, 8 August 2012 (UTC)
thread_title: Merge

message: There needs to be a drawing of a set of arbitrary bases (duals), in the context of an orthogonal basis, representing the contravariant components alongside the covariant ones.  I'll see if I can work on it.--Charlesrkiss 07:07, 28 October 2006 (UTC)
replies: text: I plan to put soon (in maybe another week) such drawing in the article Curvilinear coordinates which I work on now. Lantonov 14:52, 23 July 2007 (UTC)
thread_title:  Coordinate Representation 

message: Covariance has a more general meaning, which is not mentioned in the article. The second chapter of J. Bjorken and S. Drell, Relativistic Quantum Mechanics, McGraw-Hill, 1964, has the titel "Lorentz Covariance of the Dirac Equation". This does not concern co- or contravariant transformation, but more generally a linear representation of Lorentztransformations. In this broader sense one uses the word "covariant", when one states that Einstein's equations or the Rarita-Schwinger-equation are covariant. --Norbert Dragon (talk) 14:34, 22 August 2008 (UTC)
replies: text: You might find the article General covariance and Lorentz covariance helpful for your inquiry into this interesting topic. By the way, it was Einstein around 1920 who coined the notion of covariance of natural laws.--LutzL (talk) 16:01, 23 August 2008 (UTC)
thread_title:  General Meaning 

message: As it stands, the subject is "summation" and the verb is "are".  The summation over all indices of a product with the same lower and upper indices are invariant to a transformation.  If I'm reading it right, the statement is correct, and it's just a verb error.  In other words, it is the summation (or to be precise, the result of the summation) that's invariant, so the correct fix is simply to change the verb to "is".  It's been ages since school, though (hence my need to read the page in the first place), so I'm not quite confident of that, and I'll leave the fix to someone who is. --Dan Wylie-Sears 2 (talk) 14:22, 28 September 2010 (UTC)
thread_title:  The summation are? 

message: The prior poster has identified one of a number of confusions in this document. It was written some time ago and has been overtaken by other related entries that do not create as much confusion. Invariants are those geometrical properties that can only be recovered by summing across all indices, their various contributing factors. Hence (if I number each equation in the article starting at 0), the vector v in the equation (0) illustrates that v is the same irrespective of coordinates primed (new) or unprimed (old).
The text leading to equation (0) has another linguistic confusion "on a chosen basis ei, related to a coordinate system xi (the basis vectors are tangent vectors to the coordinate grid)" should not be "tangent to the coordinate grid'"' but rather,  "tangents identified with/by the coordinate grid".
Leaving grammatical ambiguity aside, the introductory section lacks clarity on account of scattered motivations, and it does not help to make the covariant transformation be defined by the traditions - In Physics, as the notation that follows the by definition, gives the impression of a by-fiat convention.  Further, invariance has no direct relationship to the co/contra-variance of spatial items, so equation (0) is a mild source of confusion that is amplified by the rotation illustration.
Having said all that, physicists do inform the algebraists and geometers as to which notational conventions properly correspond to physical realities of the empirical world, as the latter have no initial bias. A re-write of the article's motivation may pick up from my remaining comments that hopefully are constructive.
I suggest to leave the article as-is but preface it with the following:Mkhomo (talk)
:The suggested text seems to be very obscurely written.  I have removed it from the article.  I agree that the lead, as currently written, is not perfect.  But it is much better than what you had inserted.  Please try to satisfy your objections in a way that at least makes the article understandable to others.  Sławomir Biały (talk) 13:19, 11 January 2013 (UTC)
thread_title:  Ambiguous Motivation 

message: " The inverse of a covariant transformation is a contravariant transformation." The inverse??? 2A01:CB0C:CD:D800:6C99:F9E9:1059:8F03 (talk) 15:57, 20 December 2021 (UTC)
thread_title:  Inverse?