## Tensor

**Tensors** are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of numerical values. The *order* (also *degree* or *rank*) 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. For example, a linear map can be represented by a matrix, a 2-dimensional array, and therefore is a 2nd-order tensor. A vector can be represented as a 1-dimensional array and is a 1st-order tensor. Scalars are single numbers and are thus zeroth-order tensors.

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### Some articles on tensor:

... The Maxwell stress functions are defined by assuming that the Beltrami stress

**tensor**tensor is restricted to be of the form The stress

**tensor**which automatically ... functions These must also yield a stress

**tensor**which obeys the specified boundary conditions ...

**Tensor**

... In computer vision, the trifocal

**tensor**(also tritensor) is a 3×3×3 array of numbers (i.e ... a

**tensor**) that incorporates all projective geometric relationships among three views ... Hence, the trifocal

**tensor**can be considered as the generalization of the fundamental matrix in three views ...

**Tensor**in The Formulation of Signorini and Fichera

... the Einstein notation is adopted) where is the elasticity

**tensor**is the infinitesimal strain

**tensor**The Cauchy stress

**tensor**has therefore the following form (5) and it is linear with respect to the ...

**Tensor**

... In mathematics, the zero

**tensor**is a

**tensor**, of any order, all of whose components are zero ... The zero

**tensor**of order 1 is sometimes known as the zero vector ... Taking a

**tensor**product of any

**tensor**with any zero

**tensor**results in another zero

**tensor**...

**Tensor**- Generalizations - Spinors

... Starting with an orthonormal coordinate system, a

**tensor**transforms in a certain way when a rotation is applied ... that is not exhibited by the transformation law for

**tensors**see orientation entanglement and plate trick ... objects that generalize the transformation law for

**tensors**in a way that is sensitive to this fact ...

### More definitions of "tensor":

- (
*noun*): A generalization of the concept of a vector.