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A repeated index, meaning a sum with no sigma written.
Also known as: Summation convention, Implicit summation, Repeated index convention, Einstein summation rule
The convention says that any index appearing twice in a term is summed over, so the summation sign is simply omitted. It is not a symbol but the absence of one, which is exactly why it has to be declared: a reader who has not been told sees a product where a sum is meant.
States that an index repeated within a single term is implicitly summed over its range, with no summation sign written.
Contexts: Mathematics
Distinguishes upper and lower indices in relativity, where a valid summation pairs one of each; a repeated index at the same level signals an error.
Contexts: Mathematics
Was introduced by Einstein in 1916 and is confined to tensor work, where the alternative is an unreadable forest of sigmas.
Contexts: Mathematics
A letter carrying the same small index letter twice within one term, one raised and one lowered, with no summation sign present.