Talk:Vector notation

I requested the creation of this article. I imagined that it would be a discussion of writing equations using the symbols of vectors such as gradients, curls, dot products, etc.. Also, I would like a discussion of how this was developed to be able to express physics/engineering equations independently of the coordinate system. A good example are the Navier Stokes equations article which expresses these equations in vector notation, indicial notation as well as Cartesian Coordinates (but not in spherical, polar, cylindrical). I planned on one day doing this myself, but I suspect it will be a while before I get to it. But I think it is a useful topic, especially since indicial notation has its own page. Slffea 23:52, 4 August 2006 (UTC)

Work in progress

Still working on this! Hit the wrong button.—Kbolino 13:59, 31 October 2007 (UTC)

Updates

I have updated this page to reflect my knowledge of the different notations as best I can and improve the organization. Some of it is solid (rectangular vectors), some of it is nearly invented (polar, cylindrical, spherical), and the rest somewhere in between. There is some information missing, such as how to write vectors in other spaces (complex space, continuous function space, polynomial space, etc.) Of course, none of it is cited--which is probably more important than the content itself. Hopefully this will provide a good starting point, from which the useful information can be referenced and improved, and the less useful (and accurate) information can be pruned.—Kbolino 08:14, 5 November 2007 (UTC)

Cross-product

132.66.22.20 changed the first sentence as follows (diff: [1])

The cross product of two vectors (in $\mathbb {R} ^{3}$ or $\mathbb {R} ^{7}$)...

to

The cross product of two vectors (in $\mathbb {R} ^{3}$ or $\mathbb {R} ^{7}$ or whatever Field)...

with the edit comment: fixed inaccurate statement in cross product - it can be from any field whatsoever.

I thought the cross-product was defined for $\mathbb {R} ^{3}$ only and the cross-product article seems to agree. Qwfp (talk) 13:41, 25 February 2008 (UTC)

Diagrams

To facilitate understanding of vectors for the more visual among us, could someone create some images illustrating like the difference between a scalar, 3d vectors, and the like? (I would except I'm not too clear myself).

Thanks. — Preceding unsigned comment added by 67.142.178.24 (talk) 04:01, 20 June 2011 (UTC)

Add example notation to "shorthand notation" (second paragraph)

I was frustrated searching for where does the notation "r with a tilde below it" come from until I noticed the line in the second paragraph that says it's shorthand notation. I think we should include an example or two. 1Minow (talk) 14:23, 22 March 2014 (UTC)

ISO Standard

ISO 80000-2:2009 recommends italic bold serif for vector variables, but an example can't be given due to limitations in Wikipedia's LaTeX implementation and my own knowledge of Wikipedia markup. So I gave the example in CSS format instead with <span style="font-family: serif; font-size: large; font-weight: bold; font-style: italic">v</span>. If anyone knows how to bold, italicize, and serif a single letter using Wikipedia's implementation of LaTeX, please revise. Adelphious (talk) 00:29, 4 April 2016 (UTC)

Operational calculus

The following was removed as off-topic:

Between 1880 and 1887, Oliver Heaviside developed operational calculus,<ref The Heaviside Operational Calculus www.quadritek.com/bstj/vol01-1922/articles/bstj1-2-43.pdf /ref> ref>Involving the D notation for the differential operator, which he is credited with creating. /ref> a method of solving differential equations by transforming them into ordinary algebraic equations which caused much controversy when introduced because of the lack of rigour in its derivation.<ref He famously said, "Mathematics is an experimental science, and definitions do not come first, but later on." He was replying to criticism over his use of operators that were not clearly defined. On another occasion he stated somewhat more defensively, "I do not refuse my dinner simply because I do not understand the process of digestion." /ref>

Note that a pipe misdirected readers away from Operational calculus ! — Rgdboer (talk) 01:57, 7 November 2019 (UTC)

Rectangular vector

The term "rectangular vector" is not used in mathematics, except maybe at low level education. As a large part of the article is based on this uncommon terminology, I have simply clarified its definition, and tagged it as {{cn}}. Nevertheless the article requires to be rewritten for making it conform to the standard terminology, and to allow sourcing it. D.Lazard (talk) 11:09, 24 April 2023 (UTC)

Felix Klein pushed for the creation of a committee to unify vector notation at the

International Congress of Mathematicians

in Rome. However, the committee was unsuccessful, which was expected. Chuckstvns (talk) 18:15, 31 January 2024 (UTC)

It was more 100 years ago. Presently the concept of a vector has been fully clarified.

I have tagged the article as {{confusing}}, as this article uses a terminology that is no more in use and is not defined in Wikipedia. IMO, the content must be merged into vector (mathematics and physics) and coordinates (mathematics) (in fact nothing in this article is not already in these articles). Moreover, the article title is also confusing, since "vector notation" is an old term for "representation of vectors or points with coordinates". D.Lazard (talk) 19:01, 31 January 2024 (UTC)