Re: Halmos Lin Algebra Problem - clarification

Many thanks to both responders. Halmos' socratic method is sometimes quite
testing!

Guy
"LuckyOne" <gwlucky@xxxxxxxxxx> wrote in message
news:1146358921.950087.280210@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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.

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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.



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