Re: Halmos Lin Algebra Problem - clarification

["LuckyOne"]

>>>> But - how could V be a vector space, whatever the scalar multiplication
> rule? Surely Rplus is not a group (no zero, no additive inverses)? Does
> Halmos' vector addition rule make the set V a comutative group?



Yes. In this case the zero element is the real number 1. If a>0, it's
inverse is 1/a.

***

I used to give this problem to my undergrads.  Halmos' statement is
absolutely true and it makes one (you) stop thinking of vectors as
pointy objects.