Talk:Euclidean vector

message: The history, as we can see from the article, is only ONE LINE.
Would someone help expand the histories?
Thank you. KaliumPropane (talk) 09:05, 4 November 2010 (UTC)
thread_title:  History of vectors reduced to just one line? 

message: I know Wikipedia is written for different readers, but this is just ridiculous. The sum of the null vector with any vector a is a (that is, 0+a=a) is way too obvious and useless to be here. I don't mind if we remind readers that 1 + 1 = 2, but 0 + 1 = 1 is a little extreme. I mean I can't understand 90% of the mathematics on Wikipedia, and even I think this is too basic. 173.183.79.81 (talk) 03:10, 30 March 2011 (UTC)
replies: text: I disagree. The existence and behavior of the null vector is central to the notion of a vector space. Without it and it's admittedly trivial-seeming behavior that 0+a=a, you don't have a linear space, you have an affine space. Plenty of times in advanced mathematics, seemingly trivial things are very important and need to be mentioned. —Ben FrantzDale (talk) 12:18, 31 March 2011 (UTC)
thread_title:  I'm getting sick of it 

message: Right now, this article has an excellent introduction, followed by an overview section that mostly repeats the same content, but with less clarity and a variety of issues (like the idea that "an arrow" is the definition).  I suggest simply removing the "overview" part of the first section (I.e., before the subsection "examples in 1 dimension").  --JBL (talk) 15:55, 28 August 2012 (UTC)
thread_title:  Why is there an overview section? 

message: Does this section have contravariant and covariant backwards?  Not only does the word contravariant seem to imply it should vary in the opposite way, but the description seems to say so to.
In other words, if the reference axes were rotated in one direction, the component representation of the vector would rotate in exactly the opposite way. Similarly, if the reference axes were stretched in one direction, the components of the vector, like the co-ordinates, would reduce in an exactly compensating way.
Why then does it say, just above that, that they "transform like the coordinates" and the give math transformation both the coordinates x'=Mx and the vector v'=Mv the same.  Also why, if they are both transformed by the forward transformation, is the need for an inverse to exist mentioned.  Combined with the fact that covariance and contravariance of vectors page give the contravariant transformation in terms of the inverse, v[fA] = A^{-1}v[f], I think this section got the transformations crossed over for part of it somehow. 207.112.55.16 (talk) 04:50, 5 February 2013 (UTC)
replies: text: I'm surprised this rather obvious mistake wasn't fixed sooner. I've gone ahead and changed it.Paulmiko (talk) 17:08, 9 March 2015 (UTC)
replies: text: I've reverted this edit. Covariant means to vary like the basis does.  Contravariant means the opposite.  The set of basis vectors is covariant (by definition), and the vector of coordinate scalars that is multiplied by the basis to get an invariant vector is contravariant.  The wording in the article is confusing and should be fixed, but the meaning must not be switched around. —Quondum 17:37, 9 March 2015 (UTC)
thread_title:  Vectors, pseudovectors, and transformations 

message: The article states: "to subtract b from a, place the end points of a and b at the same point, and then draw an arrow from the tip of b to the tip of a. That arrow represents the vector a − b, as illustrated below:".  However the section on representations tells us that the tip and the endpoint are synonymous.  I presume that it should read "place the tails of a and b at the same point" or similar (this is what is illustrated).  This subject is pretty fresh to me so I will leave it to somebody else to make the change. Kelly F Thomas (talk) 16:59, 1 April 2013 (UTC)
replies: text: Quite right.  I've made everything "head"s and "tail"s in that section.  (In general this article is something of a mishmash and needs someone to go through and sort it out.  Not volunteering, though.) --JBL (talk) 21:59, 1 April 2013 (UTC)
thread_title:  vector subtraction  

message: Please, contribute to these discussions. See also talk: Vector (mathematics and physics) #A CONCEPTDAB article is needed. Incnis Mrsi (talk) 07:58, 25 April 2013 (UTC)
thread_title:  [[WT: WikiProject Mathematics #“Vector” redirects]] and next subsection 

message: In general, a tangent vector is not the same thing as a vector. The section on viewing vectors as directional derivatives should clarify what is meant, in the context of Euclidean space.  — Preceding unsigned comment added by 99.19.84.64 (talk) 23:41, 7 November 2013 (UTC)
replies: text: I don't get your point. A more general tangent is not necessarily a vector. The tangent to a curved surface for example. But the two examples given, of a scalar valued function of position (a scalar field) and a curve parameterised by a scalar, both have well defined vector valued derivatives, even though they are not themselves vectors.--JohnBlackburnewordsdeeds 00:15, 8 November 2013 (UTC)
replies: text: If you take the identity map from Rn to Rn then the set of tangent vectors is identical to the set of vector in Rn. See Tangent space#Tangent vectors as directional derivatives. For a non-singular curved surface the tangent plane will be spanned the tangent vectors.--User:Salix alba (talk): 07:37, 8 November 2013 (UTC)
thread_title:  Tangent Vectors 

message: The hatnote refers to vectors used in Physics, but in Relativity the vectors used are Lorentzian rather than Euclidean. Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:33, 26 June 2017 (UTC)
replies: text: I agree, geometric vector would be a better title, and this article shouldn’t imply that vectors can only describe Euclidean situations. Geometric vectors need not even be metrical, e.g. displacement vectors in a generic affine space don’t have any notion of distance. –jacobolus (t) 17:49, 9 November 2022 (UTC)
thread_title:  Geometric vectors are not always Euclidean 

message: In order to enable a larger group of readers to understand what is happening in the 'explanation' of the subtraction of vectors, I added extra explanations. Obviously I disagree with the removal of my additions. As it stands now, I think that too many readers won't understand it. Bob.v.R (talk) 22:41, 14 January 2019 (UTC)
replies: text: The description given now is extremely simple.  Your additions complicated it by tying the definition of subtraction to the definition of opposite and of vector addition.  But that is not necessary, and doing so diluted the point of the paragraph (which is to define vector subtraction).  --JBL (talk) 22:50, 14 January 2019 (UTC)
replies: text: I agree with JBL. Your text would make sense in a context where operations on vectors would be defined geometrically (that is coordinate free). As the choice here is to start from coordinates, one has not to prove again the properties; one has only to show that the geometrical definition is equivalent with the algebraic definition. So, your addition is confusing. D.Lazard (talk) 23:19, 14 January 2019 (UTC)
replies: text: That the definition of subtraction should be based on the definitions of opposite and of vector addition is indeed the case, in my opinion. And in that way a reader who is new to the topic will understand how subtraction of vectors is defined, though it would still be better if an illustration would be added that shows the construction of (-b) + a. In the current version there is a drawing where a vector is constructed based on two other vectors, and then it is stated that this third vector is in fact a − b. So, clearly lacking is any explanation as to why this construction should be a − b. In fact, in the current text there is not even the slightest attempt to explain the construction to the reader. The reader reads a statement and that's that. Bob.v.R (talk) 00:44, 15 January 2019 (UTC)
thread_title:  Subtraction 

message: It is worth noting that "direction" of a vector is sometimes "split" into "orientation" and "sense". 195.187.99.60 (talk) 09:18, 8 September 2020 (UTC)
thread_title:  Orientation and sense