- #1

FilipVz

- 8

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can somebody help me with the problem:

Suppose that in a vector space over field of real numbers a positive defined norm is defined for each vector which satisfies the triangle inequality and ||aU||=|a|*||u||. Show that a real valued scalar product can de defined as follows:

(U,V)=1/2*(||U+V||^2 - ||U||^2- ||V||^2)

which satisfied the postulates, if following identity is satisfied by the norms:

||U+V||^2 + ||U-V||^2 = 2*||U||^2 + 2*||V||^2