> ok, here's the problem.. prove <u,v> = 0 iff ||u||
> less than or equal
> to ||u + av||
> where u,v in V and a is in F.
> --
>
> so, <u,v> = 0 iff <v, u> = 0
> squaring both sides ||u|| ^2 = ||u|| ^2 + |a|^2
> ||v||^2
Surely you know better than that! (a+ b)^2 is NOT a^2+ b^2, it is a^2+
2ab+ b^2.
> = <u + av, u +
> = <u + av, u + av>
> = <u, u> + a
> = <u, u> + a <v,v> + .....?
>
> it is a simple problem, and any pointers to solution
> will be
> appreciated.
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