Product (mathematics)
Scalar product

A scalar product is a bi-linear map:

with the following conditions, that v ⋅ v > 0 {\displaystyle v\cdot v>0} for all 0 ≠ v ∈ V {\displaystyle 0\not =v\in V}.

From the scalar product, one can define a norm by letting ‖ v ‖:= v ⋅ v {\displaystyle \|v\|:={\sqrt {v\cdot v}}}.

The scalar product also allows one to define an angle between two vectors:

In n {\displaystyle n} -dimensional Euclidean space, the standard scalar product (called the dot product) is given by:
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