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Einstein rule

From Encyclopedia of Mathematics
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A convention for writing in a condensed form (without the summation symbol ) 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 and are written in the form and , respectively; here . 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. L.P. Kuptsov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Einstein_rule&oldid=11443
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098