nLab Einstein summation convention

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 $v_i e^i \coloneqq \sum_{1 \le i \le n} v_i e^i$.

Related entries

• Kronecker delta

• Levi-Civita symbol

• string diagram

• Feynman slash notation

References

See also

• Wikipedia, Einstein notation