Einstein summation convention

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Revision as of 10:05, 28 November 2005

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

Here are two examples:

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

$u_j\frac{\partial u_i}{\partial x_j} \equiv \sum_{j=1}^3 u_j\frac{\partial u_i}{\partial x_j} \equiv u_1\frac{\partial u_i}{\partial x_1} + u_2\frac{\partial u_i}{\partial x_2} + u_3\frac{\partial u_i}{\partial x_3}$

Revision as of 10:04, 28 November 2005 (view source) Jola (Talk \| contribs) ← Older edit		Revision as of 10:05, 28 November 2005 (view source) Jola (Talk \| contribs) Newer edit →
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-	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.	+	The Einstein summation convention is a tensor notation which is commonly used to implicitly define a sum. The convention states that when an index is repeated in a term that implies a sum over all possible values for that index.

	Here are two examples:		Here are two examples:

Einstein summation convention

From CFD-Wiki

Revision as of 10:05, 28 November 2005

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