Definition, Meaning & Anagrams | English word TENSOR

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Definitions of TENSOR

1. To compute the tensor product of two tensors.
2. (muscle) A muscle that tightens or stretches a part, or renders it tense. [from 17th c.]
3. (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array. [from 18th c.]
4. (mathematics, obsolete) A norm operation on the quaternion algebra.

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Examples of Using TENSOR in a Sentence

• A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold.
• Spin tensor, a tensor quantity for describing spinning motion in special relativity and general relativity.
• Multilinear subspace in multilinear algebra, a subset of a tensor space that is closed under addition and scalar multiplication.
• For example, in general relativity, the gravitational field is described through the metric tensor, which is a tensor field with one tensor at each point of the space-time manifold, and each belonging to the tensor product of the cotangent space at the point with itself.
• The term sedenion is also used for other 16-dimensional algebraic structures, such as a tensor product of two copies of the biquaternions, or the algebra of 4 × 4 matrices over the real numbers, or that studied by.
• The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.
• More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor.
• In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds.
• Scalar fields are contrasted with other physical quantities such as vector fields, which associate a vector to every point of a region, as well as tensor fields and spinor fields.
• The label "pseudo-" can be further generalized to pseudoscalars and pseudotensors, both of which gain an extra sign-flip under improper rotations compared to a true scalar or tensor.
• Therefore, a tangent vector of a smooth curve will transform as a contravariant tensor of order one under a change of coordinates.
• While the notion of a metric tensor was known in some sense to mathematicians such as Gauss from the early 19th century, it was not until the early 20th century that its properties as a tensor were understood by, in particular, Gregorio Ricci-Curbastro and Tullio Levi-Civita, who first codified the notion of a tensor.
• In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers defined from the sign of a permutation of the natural numbers , for some positive integer.
• In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual.
• Tensor contraction, an operation on one or more tensors that arises from the natural pairing of a finite-dimensional vector space and its dual.
• In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed tensor will be a subscript (covariant) and at least one of the indices will be a superscript (contravariant).
• In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.
• However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.
• Technically, the Fock space is (the Hilbert space completion of) the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space ,.
• A simple tensor (also called a tensor of rank one, elementary tensor or decomposable tensor) is a tensor that can be written as a product of tensors of the form.

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