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Can we please get a better definition of vector?  The one given is just terrible -- "a magnitude and a direction?"  I mean, really.  :)  --[[User:JBL|JBL]] 11:03, 1 October 2006 (EDT)

I can say that a vector is an element of a vector space (and then define vector space in a separate article, if there isn't one already), if you really that would make anything clearer :) --[[User:ComplexZeta|ComplexZeta]] 17:01, 1 October 2006 (EDT)

Yes, this article does need a ton of work.  I'll add a little here and there when I get a chance.  Heh, I think we should do more than just say a vector is an element of a vector space ;) --[[User:Joml88|Joe]] 09:42, 2 October 2006 (EDT)

No, "a member of a vector space" probably isn't fabulous.  But, for example, "an ordered tuple of numbers" is far better: "magnitude + direction" essentially limits us to real, finite vector spaces and is also totally unclear about what it means.  "Directed line segment" might be even better, because it is actually concrete.  What do you think about something like this:
"The word vector has many different definitions, depending on who is defining it and in what context.  Physicists will often refer to a vector as "a quantity with a direction and magnitude."  For Euclidean geometers, a vector is essentially a directed line segment.  In many situations, a vector is best considered as an n-tuple of numbers (often real or complex).  Most generally, but also most abstractly, a vector is any object which is an element of a given vector space."
--[[User:JBL|JBL]] 10:20, 7 October 2006 (EDT)

Also, there is an article titled "Vector Space," but it is lacking any actual content -- we definitely should fill it out, too.  --[[User:JBL|JBL]] 10:22, 7 October 2006 (EDT)

OK, vectors are closely tied to [[matrices|matrix]], which you see doesn't have a page either. Could ya'll possibly make something on matrices and [[determinant]]s and things like that, because I'm not sufficiently good at such things. --[[User:Solafidefarms|solafidefarms]] 12:02, 8 October 2006 (EDT)