### What does **tensor** mean?

# Definitions for tensor

ˈtɛn sər, -sɔrten·sor

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **tensor**.

### Princeton's WordNet

tensornoun

a generalization of the concept of a vector

tensornoun

any of several muscles that cause an attached structure to become tense or firm

### Wiktionary

tensornoun

A muscle that stretches a part, or renders it tense.

tensornoun

the image of a tuple under a tensor product map

tensornoun

a function of several variables which is a product of a number of functions of one variable, one for each variable, each of which is linear in that variable

tensornoun

a matrix of matrices

tensorverb

To compute the tensor product of something with something else

tensoradjective

Of or relating to tensors

### Wikipedia

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tensor, curvature tensor, ...) and others. In applications, it is common to study situations in which a different tensor can occur at each point of an object; for example the stress within an object may vary from one location to another. This leads to the concept of a tensor field. In some areas, tensor fields are so ubiquitous that they are often simply called "tensors". Tullio Levi-Civita and Gregorio Ricci-Curbastro popularised tensors in 1900 – continuing the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others – as part of the absolute differential calculus. The concept enabled an alternative formulation of the intrinsic differential geometry of a manifold in the form of the Riemann curvature tensor.

### ChatGPT

tensor

A tensor is a mathematical object used in physics and engineering that is an extension of scalars, vectors, and matrices. It can be represented as an array of numbers arranged in a grid that can transform according to certain rules under a change of coordinates. Tensors can represent various physical quantities such as the curvature of space-time in general relativity or the strain of a material in mechanics.

### Webster Dictionary

Tensornoun

a muscle that stretches a part, or renders it tense

Tensornoun

the ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor

### Freebase

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 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 0th-order tensors. Tensors are used to represent correspondences between sets of geometric vectors. For example, the stress tensor T takes a direction v as input and produces the stress T on the surface normal to this vector for output thus expressing a relationship between these two vectors, shown in the figure. Because they express a relationship between vectors, tensors themselves must be independent of a particular choice of coordinate system. Taking a coordinate basis or frame of reference and applying the tensor to it results in an organized multidimensional array representing the tensor in that basis, or like it looks from that frame of reference. The coordinate independence of a tensor then takes the form of a "covariant" transformation law that relates the array computed in one coordinate system to that computed in another one. This transformation law is considered to be built into the notion of a tensor in a geometric or physical setting, and the precise form of the transformation law determines the type of the tensor.

### Entomology

Tensor

a muscle which stretches a membrane.

### Anagrams for tensor »

nestor

sterno

strone

stoner

### Numerology

Chaldean Numerology

The numerical value of tensor in Chaldean Numerology is:

**8**Pythagorean Numerology

The numerical value of tensor in Pythagorean Numerology is:

**1**

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## Translations for **tensor**

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"tensor." *Definitions.net.* STANDS4 LLC, 2023. Web. 2 Dec. 2023. <https://www.definitions.net/definition/tensor>.

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