Einstein rule

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.