Q1. Does every vector space V (over R or C) have an inner product? (Finite dimensional ones do, of course.)
Q2. There are vector spaces V that have a norm ||x|| that cannot arise from any inner product < , > in the sense that <x,x> = ||x||^2 for all x. Example? #math #algebra
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I don’t believe that the taxicab norm can arise from an inner product.. its norm violates the linearity axiom of inner products
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