nLab
Einstein summation convention

Context

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

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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 nn-dimensional vector vv and covector ee, we write v ie i 1inv ie iv_i e^i \coloneqq \sum_{1 \le i \le n} v_i e^i.

References

See also

Last revised on October 16, 2017 at 11:25:54. See the history of this page for a list of all contributions to it.