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Topic: difference between a vector and a point (in R^n)
Replies: 12   Last Post: Sep 2, 2013 7:41 PM

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 FredJeffries@gmail.com Posts: 1,845 Registered: 11/29/07
Re: difference between a vector and a point (in R^n)
Posted: Aug 26, 2013 1:54 PM

On Monday, August 26, 2013 8:51:00 AM UTC-7, lite.o...@gmail.com wrote:
> What is the difference between a vector and a point?
> Why are there two concepts?
>
> Wessel described complex numbers as "vectors" in some space like R^2.
> Argand described complex numbers are "points" in some space like R^2.
>
> What's the difference?
>
> What's wrong with me saying "a vector is a point, and a point is a vector" ?

A vector is an element of a vector space:
http://en.wikipedia.org/wiki/Vector_space

R^n is a vector space. Therefore it's elements are vectors. So,
in answer to the question in the subject line, in R^n there
is no difference.

But there are many other important vector spaces, the elements
of which may not be points in the normal sense of the word.
For instance, the space of all continuous functions from
R to R. There a vector is a function.
Or the vector space of 7 x 3 matrices.

Also, there are many sets of points which are not vector spaces,
for instance (as has been pointed (pun intended) out) the
interval [0, 1]