Recent content by CB14

Sorry to open up an old thread, but I've come across this problem in my studies and have some questions about it. I was wondering if it should be taken into consideration that a field of two elements treats addition and multiplication (though I'm only looking at addition for this problem)...

Thanks for clarifying about the hint. I see now what you were saying, gopher_p. Using the parallelogram law, then, (where I'm still using |x| to denote the sup norm...must learn Latex!) |x+y|2+|x−y|2 = 2|x|2 +2|y|2 But x=e1 and y=e2, so the parallelogram law clearly isn't satisfied and...

From my understanding, I think the hint is asking us to assume this property is true (it's clearly not, of course) and in showing that it doesn't hold, it should prove that the sup norm isn't derived from the inner product. Revising my argument, if I expanded <x+y, x+y>, I would get <x, x> +...

Thanks for the reply! I checked the hint once again, but no, everything is exactly as I've written it as far as the question and the hint are concerned. I used the part of the hint where x=e1 (so x1=1, x2=0) and y=e2. In the book it says that the sup norm is calculated as follows: |x|=...

Homework Statement Show that the sup norm on R2 is not derived from an inner product on R2. Hint: suppose <x,y> is an inner product on R2 (not the dot product) and has the property that |x|=<x,y>0.5. Compute <x±y, x±y> and apply to the case x=e1, y=e2.Homework Equations |x|=<x,y>0.5 I've...