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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Defining scalar product from norm

**Physics Forums | Science Articles, Homework Help, Discussion**