Difference between revisions of "Tensor"
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== Description == | == Description == | ||
| − | Elementary examples of such relations include the dot product, the cross product, and linear maps. | + | Elementary examples of such relations include the [[dot product]], the [[cross product]], and [[Linear map|linear maps]]. |
Euclidean vectors, often used in physics and engineering applications, and scalars themselves are also tensors. | Euclidean vectors, often used in physics and engineering applications, and scalars themselves are also tensors. | ||
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* [https://en.wikipedia.org/wiki/Tensor Tensor] @ Wikipedia | * [https://en.wikipedia.org/wiki/Tensor Tensor] @ Wikipedia | ||
* [https://en.wikipedia.org/wiki/Glossary_of_tensor_theory Glossary of tensor theory] | * [https://en.wikipedia.org/wiki/Glossary_of_tensor_theory Glossary of tensor theory] | ||
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| + | [[Category:Mathematics]] | ||
| + | [[Category:Tensors]] | ||
Latest revision as of 17:23, 15 April 2016
Tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
Description
Elementary examples of such relations include the dot product, the cross product, and linear maps.
Euclidean vectors, often used in physics and engineering applications, and scalars themselves are also tensors.
A more sophisticated example is the Cauchy stress tensor T, which takes a direction v as input and produces the stress T(v) on the surface normal to this vector for output, thus expressing a relationship between these two vectors.
In terms of a coordinate basis or fixed frame of reference, a tensor can be represented as an organized multidimensional array of numerical values.
The order (also degree) of a tensor is the dimensionality of the array needed to represent it, or equivalently, the number of indices needed to label a component of that array.
See also
External links
- Tensor @ Wikipedia
- Glossary of tensor theory
