Definition talk:Vector/Real Euclidean Space

In answer to your "lots to do" question, I'd say: get it written first, then we can restructure it according to what it looks like when it's done. This is the work I have consistently shied away from because I haven't a clue where to start. So: good job, and all that. --prime mover 09:12, 29 January 2012 (EST)

That's the beauty of being a student: Since I know so much less than the experienced mathematicians, there's a lot less I can do instead of the hard stuff. --GFauxPas 09:13, 29 January 2012 (EST)

Rewrite in progress

This page is to be subsumed into Definition:Vector Quantity. The "Euclidean" nature of the space into which it is embedded is taken for granted, and is to be explained under Parallelogram Law, which applies if and only if said space is in fact Euclidean (it's explained in one of my texts on the subject, probably Weatherburn or Durell, possible McCrea -- there's something to be said for the old-fashioned viewpoint). The examples of $\R^1$, $\R^2$ and $\R^3$ are to be presented there. --prime mover (talk) 12:43, 21 October 2020 (UTC)

No, sorry, that's a rubbish idea. What we want is for there to be a page defining a strictly geometric entity, which is concerned solely with lines in space, which may or may not be higher-dimensional. Then we note that "vector quantity" can be identified with such a "space vector" / "plane vector" accordingly, and so we can apply the results that we can apply to vectors treated geometrically to "vector quantities". Before that all happens I'm reviewing all the links from this page to see what may need to be done. May in fact leave it all as it is, but just tighten up the intellectual connections between that and this. "Plane Vector" and "Space Vector" could be what we need to define the entities in $\R^2$ and $\R^3$ though. --prime mover (talk) 13:31, 21 October 2020 (UTC)