nLab Einstein summation convention

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Context

Monoidal categories

monoidal categories

Contents

Idea

In situations such as the tensor calculus, the Einstein summation convention allows for compact expression of sums over common upper and lower indices. For example, for $n$-dimensional vector $v$ and covector $e$, we write $v_i e^i \coloneqq \sum_{1 \le i \le n} v_i e^i$.