# Einstein rule

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A convention for writing in a condensed form (without the summation symbol $\sum$) a finite sum in which every term contains the summation index twice: once as an upper, and once as a lower index. Thus, the sums $\sum_{i=1}^nx^ie_i$ and $\sum_{i,j=1}^nx^iy^ja_{ij}$ are written in the form $x^ie_i$ and $x^iy^ia_{ij}$, respectively; here $1\leq i,j\leq n$. The requirement that the indices should be written on different levels is sometimes dropped.

This rule was proposed by A. Einstein (1916).

#### Comments

Also called the Einstein (summation) convention or simply the summation convention. It is mainly used in physics and differential geometry.

How to Cite This Entry:
Einstein rule. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Einstein_rule&oldid=32064
This article was adapted from an original article by L.P. Kuptsov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article