Definition talk:Dot Product

Equivalence

Please bring me up to the topic. Which way is it? Does Equivalence of Definitions of Dot Product show the equivalence or not?--Julius (talk) 13:11, 10 May 2023 (UTC)

When you restrict the context of Definition 1 to the domain of Definition 2, the definitions coincide. When the context is not a real Euclidean space, this is not the case.

We still need to establish the precise characteristics of a norm on such a normed vector space in which the cosine definition hold, or whether it can be strictly demonstrated that the norm has to be the Euclidean norm, as has currently been assumed. All we have now is that the taxicab norm is not valid as such a norm. --prime mover (talk) 15:09, 10 May 2023 (UTC)