A norm on a vector space U is a function k kW U ! 0;1/ suchthat kuk D 0 if and only if u
Chapter 6, Problem 21(choose chapter or problem)
A norm on a vector space U is a function k kW U ! 0;1/ suchthat kuk D 0 if and only if u D 0, kukDjjkuk for all 2 Fand all u 2 U, and ku C vkkukCkvk for all u; v 2 U. Provethat a norm satisfying the parallelogram equality comes from an innerproduct (in other words, show that if k k is a norm on U satisfying theparallelogram equality, then there is an inner product h ; i on U suchthat kukDhu; ui1=2 for all u 2 U).
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