Talk:Scalar (mathematics)

message: A recent edit expanded the definition as follows:
:"In mathematics and especially in linear algebra, the term scalar is frequently used to denote an ordinary real or complex number in order to clearly distinguish such numbers from other numerical objects such as vectors and matrices. Central to the subject is the notion of a vector space, which relates scalars to these objects through the operation of scalar multiplication. Multiplying a vector by a scalar has the effect of scaling it (changing its length), hence the choice of term.More generally, the set of scalars associated with a vector space may be any field. In abstract algebra the notion of vector space is itself generalised by that of a module, in which the scalars may come from any ring."
I mostly reverted these two paragraphs to the original form.  It seems inappropriate for a mathematics article  to give priority to the informal and fuzzy sense of the term (which, by the way, was already listed further down in the head section) over the precise sense (which got largely lost in the rewrite).   Note that the informal sense is almost surely derived from the precise one (namely, 1x1 matrices are informally called scalars because they behave like elements of the scalar field), not the other way around.Also, the details on what fields can be scalars are better left for the appropriate section.Jorge Stolfi 16:33, 9 January 2006 (UTC)
replies: text: I'd say your current introductory paragraph is considerably less useful than the ones you reverted and quoted above.  It provides no insight at all as to the significance or rationale of the concept and is bound to be all but meaningless to anyone who is not a mathematician (to mathematicians it's merely a very poorly phrased tautology - do we multiply scalars "into" things? do we call the elements of modules "vectors"?).  I'll leave it to other objective parties to compare the two, though.   — merge 04:05, 12 January 2006 (UTC)
replies: text: The rationale, if needed, should be added in the article body, as in other methematical articles. As for the style, and vector in modules, I have rewritten it again; please check. (BTW, what was wrong with "multiply into")? Jorge Stolfi 08:33, 14 January 2006 (UTC)
thread_title: Main sense should be the (precise) linear algebra sense

message: The suggestion that the "scalars" have that name because they "scale" (i.e. "change the scale") of vectors sounds plausible, but does not seem consistent with Hamilton's quote; so it may be just folk etymology.  It may well be  that the verb "to scale (up/down)" and the noun/adjective "scalar" evolved from the noun "scale" by separate routes: the former possibly among draftsmen and geometers, from the "scale of a drawing", the latter in algebra as per Hamilton's justification.Jorge Stolfi 16:33, 9 January 2006 (UTC)
thread_title: Etymology of scalar

message: The introduction says : "...a scalar is a number..." I'm not very comfortable with that statement. A scalar need not be a number in any ususal (however general) sense of the word. I think it should be reworded somehow. --Meni Rosenfeld 07:03, 12 January 2006 (UTC)
replies: text: I agree and hence I edited the intro slightly. -- Jitse Niesen (talk) 13:43, 12 January 2006 (UTC)
replies: text: You are right. The only fields I have ever seen used as scalars were either subfields of the complex numbers, or the integer numbers modulo a prime power.  However, ther are weirder fields around (such as rational functions of a variable X).  I have reworked the head paragraph again. See if it is better now.  All the best, --Jorge Stolfi 08:29, 14 January 2006 (UTC)
thread_title:  Is "scalar" a number? 

message: I have added a parag about every vector space being isomorphic to a coordinate space over its scalar field.  Did I get it right? Thanks, --Jorge Stolfi 08:29, 14 January 2006 (UTC)
thread_title: Basis theorem

message: Hi.  I've significantly refactored this article to improve organisation and tried to clarify some of the text, as well as simplify the intro per a suggestion from Jitse Niesen.  If I inadvertently removed an important piece of information that someone added, I'd be grateful if you'd add it back in.  Thanks!   — merge 15:55, 20 February 2006 (UTC)
thread_title:  Refactoring 

message: Particularly due to the encyclopedic nature of Wiki content, Mathematical articles should always possess an "Examples" section, for hard-examples or tangible definitions of the product in question.-68.148.73.203 (talk) 10:51, 16 November 2009 (UTC)
thread_title:  Examples 

message: I found the following entry in the page on magnitude:
*Scalar (mathematics), a quantity defined only by its magnitude
Even though this article says scalars can be negative. 24.85.161.72 (talk) 20:07, 4 August 2012 (UTC)
thread_title:  disambugation page [[magnitude]] 

message: In the section Definitions and properties, subsection Scalars of vector spaces, second paragraph, the last part of the sentence appears to be ungrammatical and, thus, unintelligible: "The scalars can be taken from any field, including the rational, algebraic, real, and complex numbers, as well as finite fields. a number by the elements inside the brackets."  Wikifan2744 (talk) 21:33, 22 September 2014 (UTC)
thread_title:  Ungrammatical sentence