Overview
The dot product is an instance of an inner product. It is typically defined as the sum of componentwise multiplication. That is,
{% \vec{A} \cdot \vec{B} = (A^1B^1, A^2B^2, A^3B^3) %}
{% \vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{B} %}
{% \vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{B} %}