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Einstein summation convention

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Revision as of 09:50, 28 November 2005

The Einstein summation convention is a tensor notation which is commonly used to implicitly define a sum. The convention states that as soon as one index is repeated in a term that implies a sum over all possible values for that index.

Here is an example:


\frac{\partial u_i}{\partial x_i} \equiv \sum_{i=1}^3 \frac{\partial u_i}{\partial x_i} \equiv \frac{\partial u_1}{\partial x_1} + \frac{\partial u_2}{\partial x_2} + \frac{\partial u_3}{\partial x_3}
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