\begin{definition}[Definition:Dot Product/Einstein Summation Convention]
Let $\mathbf a$ and $\mathbf b$ be vector quantities.
The dot product of $\mathbf a$ and $\mathbf b$ can be expressed using the Einstein summation convention as:
{{begin-eqn}}
{{eqn | l = \mathbf a \cdot \mathbf b 
      | o = :=
      | r = a_i b_j \delta_{i j}
      | c = 
}}
{{eqn | r = a_i b_i
      | c = 
}}
{{eqn | r = a_j b_j
      | c = 
}}
{{end-eqn}}
where $\delta_{i j}$ is the Kronecker delta.
\end{definition}