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Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Mathematical operation on vector spaces
called the tensor product of v and w. An element of V⊗W is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable
Tensor_product
Series of system-on-chip processors
2020. The first-generation Tensor chip debuted on the Pixel 6 smartphone series in 2021, and was succeeded by the Tensor G2 chip in 2022, G3 in 2023
Google_Tensor
Topics referred to by the same term
objects related to a vector space. Tensor may also refer to: Tensor (intrinsic definition) Tensor field Tensor product Tensor (obsolete), the norm used on the
Tensor_(disambiguation)
Assignment of a tensor continuously varying across a region of space
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space
Tensor_field
Tensor describing energy momentum density in spacetime
stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor field quantity
Stress–energy_tensor
Muscle of the thigh
The tensor fasciae latae (or tensor fasciæ latæ or, formerly, tensor vaginae femoris) is a muscle of the thigh. Together with the gluteus maximus, it acts
Tensor_fasciae_latae_muscle
Field-equations in general relativity
Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum
Einstein_field_equations
In mathematics, the tensor representations of the general linear group are those that are obtained by taking finitely many tensor products of the fundamental
Tensor_representation
Tensor used in general relativity
differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature
Einstein_tensor
Tensor field in Riemannian geometry
mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the
Riemann_curvature_tensor
Structure defining distance on a manifold
metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g ( v , v ) >
Metric_tensor
Muscle of the middle ear
stapedius. The tensor tympani is supplied by the tensor tympani nerve, a branch of the mandibular branch of the trigeminal nerve. As the tensor tympani is
Tensor_tympani_muscle
Topics referred to by the same term
Look up tense in Wiktionary, the free dictionary. Tense may refer to: Grammatical tense, a property of verbs indicating chronology Tense–aspect–mood, a
Tense
Stress-strain relation in a linear elastic material
elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness
Elasticity_tensor
Mathematical object that describes the electromagnetic field in spacetime
electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a tensor that describes
Electromagnetic_tensor
Concept in machine learning
("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations
Tensor_(machine_learning)
AI accelerator ASIC by Google
The Tensor Processing Unit (TPU) is a neural processing unit (NPU) application-specific integrated circuit (ASIC) developed by Google for neural network
Tensor_Processing_Unit
Representation of mechanical stress at every point within a deformed 3D object
Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress
Cauchy_stress_tensor
Visual aid used in mathematics
In scientific visualization a tensor glyph is an object that can visualize all or most of the nine degrees of freedom, such as acceleration, twist, or
Tensor_glyph
Tensor Tech is a Taiwanese space technology company. Tensor Tech founder Thomas Yen claims that the initial motor design was inspired by a futuristic
Tensor_Tech
Graph representation in quantum mechanics
compression and contraction are both efficient. Tensor network states are the special case in which a tensor network represents a variational wave function
Tensor_network
Tensor index notation for tensor-based calculations
notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern
Ricci_calculus
Concept in mathematics
In mathematics, the tensor-hom adjunction is the statement that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ( X , − ) {\displaystyle
Tensor–hom_adjunction
Tensor equal to the negative of any of its transpositions
tensor is antisymmetric with respect to its first three indices. If a tensor changes sign under exchange of each pair of its indices, then the tensor
Antisymmetric_tensor
Topics referred to by the same term
Tensing may refer to: Tenseness (or tensing), a concept in the linguistic fields of phonetics and phonology Ten Sing, a Christian youth program Tenzing
Tensing
Measure of the curvature of a pseudo-Riemannian manifold
Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann
Weyl_tensor
Tensor in general relativity
In mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields
Killing_tensor
Conservation law
The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after Josef-Maria Jauch and Edward Lee Hill and David M. Fradkin, is a conservation law used in
Fradkin_tensor
Topics referred to by the same term
In differential geometry, the term curvature tensor may refer to: the Riemann curvature tensor of a Riemannian manifold — see also Curvature of Riemannian
Curvature_tensor
Topics referred to by the same term
Tensor category (within the subfield category theory of mathematics) may refer to: General monoidal categories; or More specifically symmetric monoidal
Tensor_category
Physical quantity that expresses internal forces in a continuous material
the first and second Piola–Kirchhoff stress tensors, the Biot stress tensor, and the Kirchhoff stress tensor. Bending Compressive strength Critical plane
Stress_(mechanics)
Universal construction in multilinear algebra
the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any order) with multiplication being the tensor product
Tensor_algebra
Tensor in differential geometry
converge. Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric
Ricci_curvature
Topics referred to by the same term
A tensor muscle has the function of tensing (stretching or tightening) a part and may refer to: Tensor fasciae latae muscle Tensor tympani muscle Tensor
Tensor_muscle
Mathematical model for describing material deformation under stress
deformation tensors. In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor (the
Finite_strain_theory
Generalization of tensor fields
differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing
Tensor_density
American skateboarding truck company
Tensor Trucks is an American skateboarding truck company founded and designed by professional skateboarder, Rodney Mullen, in 2000. Tensor's parent company
Tensor_Trucks
Cotton tensor on a pseudo-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric tensor. The vanishing of the Cotton tensor for
Cotton_tensor
Coordinate-free definition of a tensor
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
Tensor_(intrinsic_definition)
Object in differential geometry
The contorsion tensor (or contortion tensor) in differential geometry is the difference between a connection with and without torsion in it. It commonly
Contorsion_tensor
Method of constructing an image from multiple viewpoints
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
Trifocal_tensor
Open-source software library for LLM inference
UINT64 // starting position within the tensor_data block, relative to the start of the block // (n+1)-th tensor ... Llama.cpp supports many large language
Llama.cpp
Type of monoidal category
collection of tensors. There are several equivalent alternative ways of defining modular tensor categories. One definition is as follows: a modular tensor category
Modular_tensor_category
Process in algebra
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting
Tensor_decomposition
Image upscaling technology by Nvidia
13, 2024. "On Tensors, Tensorflow, And Nvidia's Latest 'Tensor Cores'". tomshardware.com. April 11, 2017. Retrieved April 8, 2020. "Tensor Core DL Performance
Deep_Learning_Super_Sampling
Operation in mathematics
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. This example
Tensor_contraction
Abbreviation in the fields of special and general relativity
relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. General four-tensors are usually written in tensor index notation
Four-tensor
Tensor invariant under permutations of vectors it acts on
In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T (
Symmetric_tensor
Class of mathematical software
similar to MATLAB and GNU Octave, but designed specifically for tensors. Tensor is a tensor package written for the Mathematica system. It provides many
Tensor_software
Tensor related to gradients
structure tensor is often used in image processing and computer vision. For a function I {\displaystyle I} of two variables p = (x, y), the structure tensor is
Structure_tensor
Tensor having both covariant and contravariant indices
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
Mixed_tensor
Tensor operator generalizes the notion of operators which are scalars and vectors
graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which
Tensor_operator
Force needed to pull a spring grows linearly with distance
is a fourth-order tensor (that is, a linear map between second-order tensors) usually called the stiffness tensor or elasticity tensor. One may also write
Hooke's_law
Decomposition in multilinear algebra
multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal
Tensor_rank_decomposition
Concept in mathematics
In mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold
Tensor_bundle
Representation of a tensor in Euclidean space
a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from
Cartesian_tensor
Pronunciation of a sound with greater muscular effort than normal
see IPA § Brackets and transcription delimiters. In phonology, tenseness or tensing is, most generally, the pronunciation of a sound with greater muscular
Tenseness
Muscle of the soft palate
The tensor veli palatini muscle (tensor palati or tensor muscle of the velum palatinum) is a thin, triangular muscle of the head that tenses the soft palate
Tensor_veli_palatini_muscle
Antisymmetric permutation object acting on tensors
independent of any metric tensor and coordinate system. Also, the specific term "symbol" emphasizes that it is not a tensor because of how it transforms
Levi-Civita_symbol
the infinite tensor product generalizes the tensor product to possibly infinite families of associative algebras. The infinite tensor product of a family
Infinite_tensor_product
Operation that pairs a left and a right R-module into an abelian group
universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. The tensor product of an algebra and
Tensor_product_of_modules
Tensor that describes the 4D geometry of spacetime
manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Orientational order parameter
liquid phase. The Q {\displaystyle \mathbf {Q} } tensor is a second-order, traceless, symmetric tensor and is defined by Q = S ( n ⊗ n − 1 3 I ) + R (
Q-tensor
In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles S m n = d e f 1 N ∑ i = 1 N
Gyration_tensor
Fictional archmage from Dungeons & Dragons
the Dungeons & Dragons roleplaying game, Tenser is an archmage who strives to rid the Flanaess of evil. Tenser is a former member of both the Citadel of
Tenser
Rank-3 tensor in general relativity associated with gauge fields
The Lanczos tensor or Lanczos potential is a rank 3 tensor in general relativity that generates the Weyl tensor. It was first introduced by Cornelius
Lanczos_tensor
Spinning motion in theoretical physics
theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general
Spin_tensor
Machine learning software library
May 2019, Google announced TensorFlow Graphics for deep learning in computer graphics. In May 2016, Google announced its Tensor processing unit (TPU), an
TensorFlow
Hypothetical elementary particle that mediates gravity
stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally
Graviton
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of
Moment_of_inertia
Medical condition
Tonic tensor tympani syndrome is a hypothesized syndrome of the tensor tympani muscle. The tensor tympani muscle is one of the two middle ear muscles
Tonic_tensor_tympani_syndrome
Proposed theories of gravity
convention is used. ημν is the Minkowski metric. gμν is a tensor, usually the metric tensor. These have signature (−,+,+,+). Partial differentiation is
Alternatives to general relativity
Alternatives_to_general_relativity
Object in differential geometry
differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors
Torsion_tensor
mathematics and physics, a recurrent tensor, with respect to a connection ∇ {\displaystyle \nabla } on a manifold M, is a tensor T for which there is a one-form
Recurrent_tensor
energy–momentum tensor and the Petrov classification of the Weyl tensor. There are various methods of classifying these tensors, some of which use tensor invariants
Mathematics of general relativity
Mathematics_of_general_relativity
Tensor in general relativity
general relativity, the tidal tensor is generalized by the Riemann curvature tensor. In the weak-field limit, the tidal tensor is given by the components
Tidal_tensor
Concept in multilinear algebra and representation theory
and representation theory, the principal invariants of the second rank tensor A {\displaystyle \mathbf {A} } are the coefficients of the characteristic
Invariants_of_tensors
Specification of a derivative along a tangent vector of a manifold
fields) and to arbitrary tensor fields, in a unique way that ensures compatibility with the tensor product and trace operations (tensor contraction). Given
Covariant_derivative
Binary file format for storing machine-learning models
// starting position within the tensor_data block, relative to the start of the block // (n+1)-th tensor ... Tensor data follows the info block and begins
GGUF
tensor product of vector bundles E, F (over the same space X) is a vector bundle, denoted by E ⊗ F, whose fiber over each point x ∈ X is the tensor product
Tensor_product_bundle
time derivative of the angular displacement tensor, which is a second rank skew-symmetric tensor. This tensor Ω will have n(n−1)/2 independent components
Angular_velocity_tensor
Electromagnetic stress
electromagnetism, the Maxwell stress tensor (named after James Clerk Maxwell) is the stress tensor of an electromagnetic field. In tensor index notation it is given
Maxwell_stress_tensor
Mathematical operation on matrices
specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map
Kronecker_product
Mathematical model for describing material deformation under stress
tensors used in finite strain theory, e.g. the Lagrangian finite strain tensor E {\displaystyle \mathbf {E} } , and the Eulerian finite strain tensor
Infinitesimal_strain_theory
field. Tensors also have extensive applications in physics: Electromagnetic tensor (or Faraday's tensor) in electromagnetism Finite deformation tensors for
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Model of desk lamp
in 1959, and the lamp was commercialized in 1960 by the Tensor Corporation. The first Tensor lamp consisted of a 12-volt automobile light bulb and a reflector
Tensor_lamp
2025 Android smartphone developed by Google
subjects. The custom Google Tensor G5 System-on-Chip (SoC) is a noticeable upgrade over the Tensor G4 and other previous Tensor processors. Instead of using
Pixel_10
Covariant derivative of the metric tensor
In mathematics, the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It can be interpreted as the failure
Nonmetricity_tensor
{1}}}} be the second order identity tensor. Then the derivative of this tensor with respect to a second order tensor A {\displaystyle {\boldsymbol {A}}}
Tensor derivative (continuum mechanics)
Tensor_derivative_(continuum_mechanics)
the injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the
Injective_tensor_product
Method of utilizing water in magnetic resonance imaging
more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming
Diffusion-weighted magnetic resonance imaging
Diffusion-weighted_magnetic_resonance_imaging
geometry, a Codazzi tensor (named after Delfino Codazzi) is a symmetric 2-tensor whose covariant derivative is also symmetric. Such tensors arise naturally
Codazzi_tensor
Type of fluid
viscosity. The total stress tensor 𝝈 can always be decomposed as the sum of the isotropic stress tensor and the deviatoric stress tensor (𝝈′): 𝝈=13tr(𝝈) 𝐈+𝝈′
Newtonian_fluid
Graphical notation for multilinear algebra calculations
essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting
Penrose_graphical_notation
Tensor used in continuum mechanics
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed
Viscous_stress_tensor
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
thought of as a tensor, and is written δ j i {\displaystyle \delta _{j}^{i}} . Sometimes the Kronecker delta is called the substitution tensor. When juxtaposition
Kronecker_delta
Mathematical identities
𝐉𝐀=d𝐀=(∇𝐀)𝖳=(∂Ai∂xj)ij. Recursive definition of tensor: A tensor of order 0 is a scalar. A tensor of order 1 is a vector. A tensor of order 2 (also called a dyadic)
Vector_calculus_identities
Theory of brain function
a network of tensors. Sensory input = covariant tensor Motor output = contravariant tensor Cerebellar neuronal network = metric tensor that transforms
Tensor_network_theory
Deep learning library
performance across major cloud platforms. PyTorch defines a class called Tensor (torch.Tensor) to store and operate on homogeneous multidimensional rectangular
PyTorch
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travel, tourism, insurance