What is tensor?

  • (noun): Any of several muscles that cause an attached structure to become tense or firm.
    See also — Additional definitions below


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:

Trifocal 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 ...
Maxwell Stress Functions
... 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 obeys the equilibrium equation ... in terms of the stress functions These must also yield a stress tensor which obeys the specified boundary conditions ...
Tensor - Generalizations - Spinors
... Starting with an orthonormal coordinate system, a tensor transforms in a certain way when a rotation is applied ... 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 ...
Signorini Problem - Formal Statement of The Problem - The Form of The Stress Tensor in The Formulation of Signorini and Fichera
... notation is adopted) where is the elasticity tensor is the infinitesimal strain tensor The Cauchy stress tensor has therefore the following form (5 ...
List Of Zero Terms - Zero 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 ...

More definitions of "tensor":

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