# 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:
 $\ds \mathbf a \cdot \mathbf b$ $:=$ $\ds a_i b_j \delta_{i j}$ $\ds$ $=$ $\ds a_i b_i$ $\ds$ $=$ $\ds a_j b_j$
where $\delta_{i j}$ is the Kronecker delta.