Substitution Rule for Matrices/Einstein Summation Convention

Summation Convention
Let $\mathbf A$ be a square matrix of order $n$. The Substitution Rule for Matrices can be expressed using the summation convention as:
 * $(1): \quad \delta_{i j} a_{j k} = a_{i k}$
 * $(2): \quad \delta_{i j} a_{k j} = a_{k i}$

where:
 * $\delta_{i j}$ is the Kronecker delta
 * $a_{j k}$ is element $\left({j, k}\right)$ of $\mathbf A$.

The index which appears twice in these expressions is the element $j$, which is the one summated over.