Euclidean norm is defined usually as|v|(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}= g(v,v), where g is a nondegenerate, positive definite, symmetric bilinear form. But how can make it backwards? What properties must norm have that g(v,w) = (|v+w|^{2}- |v|^{2}- |w|^{2})/2 be a positive definite, symmetric bilinear form?

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# Defining scalar product from norm

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