\begin{definition}[Definition:Einstein Summation Convention]
The '''Einstein summation convention''' is a notational device used in the manipulation of matrices and vectors, in particular square matrices in the context of physics and applied mathematics.
If the same index occurs twice in a given expression involving matrices, then summation over that index is automatically assumed.
Thus the summation sign can be omitted, and expressions can be written more compactly.
\end{definition}