Talk:Vector

Can we please get a better definition of vector? The one given is just terrible -- "a magnitude and a direction?" I mean, really.  :) --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 :) --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 ;) --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" is far superior because it is actually concrete). How 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."

--JBL 10:20, 7 October 2006 (EDT)