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Process in algebra
states, and operators or tensor trains; Online Tensor Decompositions hierarchical Tucker decomposition; block term decomposition This section introduces
Tensor_decomposition
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 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)
Tensor decomposition
the higher-order singular value decomposition (HOSVD) is a misnomer. There does not exist a single tensor decomposition that retains all the defining properties
Higher-order singular value decomposition
Higher-order_singular_value_decomposition
Tensor decomposition
In mathematics, Tucker decomposition decomposes a tensor into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker although
Tucker_decomposition
In cosmological perturbation theory, the scalar–vector–tensor decomposition is a decomposition of the most general linearized perturbations of the
Scalar–vector–tensor decomposition
Scalar–vector–tensor_decomposition
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Matrix decomposition
m\times n} matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex
Singular_value_decomposition
Certain vector fields are the sum of an irrotational and a solenoidal vector field
Scalar–vector–tensor decomposition Hodge theory generalizing Helmholtz decomposition Polar factorization theorem Helmholtz–Leray decomposition used for defining
Helmholtz_decomposition
importance of the decomposition is in the properties of the three new tensors S, E, and W. Terminological note. The tensor W is called the Weyl tensor. The notation
Ricci_decomposition
Dimensionality reduction of graph-based semantic data objects [machine learning task]
interaction technique with the block term tensor format, which is a generalization of CP decomposition and Tucker decomposition. It divides the embedding vector
Knowledge_graph_embedding
Mathematical operation on vector spaces
called the tensor product of v {\displaystyle v} and w {\displaystyle w} . An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product
Tensor_product
Class of mathematical software
algebraic tensor manipulation. Tensor is an R package for basic tensor operations. rTensor provides several tensor decomposition approaches. nnTensor provides
Tensor_software
Name of two different techniques based on the singular value decomposition
generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD). The two versions
Generalized singular value decomposition
Generalized_singular_value_decomposition
Process in linear algebra
the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two
Schmidt_decomposition
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
American applied mathematician
Tensor decomposition and algorithms Jin, Ruhui; Kileel, Joe; Kolda, Tamara G.; Ward, Rachel (2024). "Scalable Symmetric Tucker Tensor Decomposition"
Tamara_G._Kolda
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
Mathematical model for describing material deformation under stress
invertible second-order tensor, can be decomposed, using the polar decomposition theorem, into a product of two second-order tensors (Truesdell and Noll,
Finite_strain_theory
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
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
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
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
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
Networks with multiple kinds of relations
}^{i\alpha }} might be named Google tensor and u j β i α {\displaystyle u_{j\beta }^{i\alpha }} is the rank-4 tensor with all components equal to 1. As
Multidimensional_network
Coordinate-free definition of a tensor
mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear
Tensor_(intrinsic_definition)
Approach to dimensionality reduction
algebra Multilinear Principal Component Analysis Tensor Tensor decomposition Tensor software Tucker decomposition M. A. O. Vasilescu, D. Terzopoulos (2003) "Multilinear
Multilinear_subspace_learning
Algorithms for matrix decomposition
negatively. Multilinear algebra Multilinear subspace learning Tensor Tensor decomposition Tensor software Dhillon, Inderjit S.; Sra, Suvrit (2005). "Generalized
Non-negative matrix factorization
Non-negative_matrix_factorization
Extracting features from raw data for machine learning
(NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The non-negativity constraints on coefficients
Feature_engineering
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
Vector operator in vector calculus
authors define the divergence of a mixed tensor by using the musical isomorphism ♯: if T is a (p, q)-tensor (p for the contravariant vector and q for
Divergence
Paradigm in machine learning that uses no classification labels
of the document is changed. It is shown that method of moments (tensor decomposition techniques) consistently recover the parameters of a large class
Unsupervised_learning
Mathematical wave functions
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks
Tensor_network
Artificial intelligence system for discovering matrix multiplication algorithms
large space of possible tensor decompositions. AlphaTensor approached this problem by representing algorithm discovery as TensorGame, in which each move
AlphaTensor
Topic in semi-Riemannian geometry
geometry, the Bel decomposition, taken with respect to a specific timelike congruence, is a way of breaking up the Riemann tensor of a pseudo-Riemannian
Bel_decomposition
Polish computer scientist (born 1947)
(NMF), tensor decomposition, Deep (Multilayer) Factorizations for ICA, NMF, neural networks for optimization problems and signal processing, Tensor network
Andrzej_Cichocki
Formulation of general relativity
we will see below). Now given any anti-symmetric tensor T I J {\displaystyle T^{IJ}} , we can decompose it as T I J = 1 2 ( T I J − i 2 ε K L I J T K L
Self-dual_Palatini_action
Concept in physics
In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e.,
Strain-rate_tensor
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
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
{\displaystyle L} . Tensor-CURT decomposition is a generalization of matrix-CUR decomposition. Formally, a CURT tensor approximation of a tensor A is three matrices
CUR_matrix_approximation
Quantum state of multiple particles represented as complex matrices
decomposition, and mixed-canonical decomposition. The decomposition of the d N {\displaystyle d^{N}} -dimensional tensor starts with the separation of the
Matrix_product_state
Topic in general relativity
perturbations of the metric: by the scalar-vector-tensor decomposition these evolve independently of the vector and tensor perturbations and are the predominant ones
Newtonian_gauge
Dimension of the column space of a matrix
with tensor order, which is called tensor rank. Tensor order is the number of indices required to write a tensor, and thus matrices all have tensor order
Rank_(linear_algebra)
Concept in mathematics
In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group
Tensor product of representations
Tensor_product_of_representations
Second-order tensor
In Riemannian geometry the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten defined for n ≥ 3 by: P = 1 n − 2 ( R i c − R
Schouten_tensor
Method of data analysis
multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (invented in the last quarter
Principal_component_analysis
Algebra associated to any vector space
alternating tensor subspace. On the other hand, the image A ( T ( V ) ) {\displaystyle {\mathcal {A}}(\mathrm {T} (V))} is always the alternating tensor graded
Exterior_algebra
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
Physicist and geneticist
Matrix and Tensor Modeling. Wiley. ISBN 978-1-119-07837-1. wikt:Citations:eigengene Alter, Orly (31 January 2020). "Multi-Tensor Decompositions for Personalized
Orly_Alter
Type of fluid
tensor σ {\displaystyle {\boldsymbol {\sigma }}} can always be decomposed as the sum of the isotropic stress tensor and the deviatoric stress tensor (
Newtonian_fluid
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
the metric tensor along an integral curve generated by the vector field (whose image is parallel to the x-axis). Furthermore, the metric tensor is independent
Killing_vector_field
Set of scalars in general relativity
the Weyl tensor.) As one might expect from the Ricci decomposition of the Riemann tensor into the Weyl tensor plus a sum of fourth-rank tensors constructed
Curvature invariant (general relativity)
Curvature_invariant_(general_relativity)
Researcher and Professor of computing
scientific machine learning and tensor methods for probabilistic models" 2022 ACM Fellow for "contributions to tensor methods for probabilistic models
Anima_Anandkumar
Mathematical theorem in representation theory
under the joint action of the groups Sk and GLn, the tensor space decomposes into a direct sum of tensor products of irreducible modules (for these two groups)
Schur–Weyl_duality
Set of integral curves of a vector field
the Bel decomposition of the Riemann tensor, taken with respect to our timelike unit vector field, the electrogravitic tensor (or tidal tensor) is defined
Congruence (general relativity)
Congruence_(general_relativity)
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
Astrophysical models for the formation of galaxies and clusters of galaxies
By the scalar-vector-tensor decomposition, the metric includes four scalar perturbations, two vector perturbations, and one tensor perturbation. Only the
Structure_formation
Aspect of general relativity
tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime manifold. The Einstein tensor is
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
Data analysis method
extended for the analysis of tensor data, in the form of L1-Tucker, the L1-norm robust analogous of standard Tucker decomposition. Two algorithms for the solution
L1-norm principal component analysis
L1-norm_principal_component_analysis
*-algebra of bounded operators on a Hilbert space
tensor product of two von Neumann algebras acting on two Hilbert spaces is defined to be the von Neumann algebra generated by their algebraic tensor product
Von_Neumann_algebra
Relative deformation of a physical body
ISO 80000-4 (Mechanics), as a "tensor quantity representing the deformation of matter caused by stress. Strain tensor is symmetric and has three linear
Strain_(mechanics)
Coefficients in angular momentum eigenstates of quantum systems
particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible
Clebsch–Gordan_coefficients
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
Mathematical identities
)^{\textsf {T}}} is a tensor field of order k + 1. For a tensor field T {\displaystyle \mathbf {T} } of order k > 0, the tensor field ∇ T {\displaystyle
Vector_calculus_identities
Calculus of vector-valued functions
(p,q)} tensor can be formed by taking a tensor product of a ( p , 0 ) {\displaystyle (p,0)} tensor and a ( 0 , q ) {\displaystyle (0,q)} tensor, which
Vector_calculus
Mathematical objects more general than vectors
{\displaystyle l} is the number of indices, i.e., tensor rank; B. Tensor is symmetric with respect to indices; C. Tensor is harmonic, i.e., it is a solution of the
Harmonic_tensors
Differential operator in mathematics
any tensor field T {\displaystyle \mathbf {T} } ("tensor" includes scalar and vector) is defined as the divergence of the gradient of the tensor: ∇ 2
Laplace_operator
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
Superenergy tensor of gravitational field flux-energy in a vacuum
In general relativity and differential geometry, the Bel–Robinson tensor is a tensor defined in the abstract index notation by: T a b c d = C a e c f C
Bel–Robinson_tensor
1)-matrix Bohemian matrices Matrix decomposition Cholesky decomposition LU decomposition QR decomposition Polar decomposition Reducing subspace Spectral theorem
Outline_of_linear_algebra
Vector operation
two tensors (multidimensional arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their tensor product
Outer_product
Mathematical physics equation tied to the Dirac current
In mathematical physics, the Gordon decomposition (named after Walter Gordon) of the Dirac current is a splitting of the charge or particle-number current
Gordon_decomposition
Operation on differential forms
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Exterior_derivative
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
Professor of Statistical Genomics
imputation, genotype calling from arrays and sequencing, sparse tensor decomposition for RNA-seq datasets, population structure, phenotype prediction
Jonathan_Marchini
Russian mathematician
He is best known for the tensor train decomposition, which is more commonly called a matrix product state in the area of tensor networks. Oseledets joined
Ivan_Oseledets
Binding of Cocaine Analogues to the Monoamine Transporters Using Tensor Decomposition 3-D QSAR". Bioorganic & Medicinal Chemistry. 10 (5): 1197–1206. doi:10
List_of_cocaine_analogues
Formula for the derivative of a ratio of functions
Stokes' Divergence Generalized Stokes Helmholtz decomposition Multivariable Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative
Quotient_rule
Notion in geometry
individually, the Weyl tensor and Ricci tensor do not in general determine the full curvature tensor, the Riemann curvature tensor can be decomposed into a Weyl
Curvature of Riemannian manifolds
Curvature_of_Riemannian_manifolds
Effective theory of gravity
the Minkowski metric, we find the standard weak field decomposition into a scalar, vector and tensor h μ ν → ( h 00 , h 0 i , h i j ) {\displaystyle h_{\mu
Non-relativistic general relativity
Non-relativistic_general_relativity
Measure of curvature in differential geometry
Riemann curvature tensor. Alternatively, in a coordinate-free notation one may use Riem for the Riemann tensor, Ric for the Ricci tensor and R for the scalar
Scalar_curvature
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
Algorithm for reducing the dimension of tensors
algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such
Tensor_sketch
Belgian engineer
working in numerical linear algebra and specializing in the study of tensor decompositions. He received a PhD in engineering from KU Leuven in 1997. He was
Lieven_De_Lathauwer
Method of utilizing water in magnetic resonance imaging
Basser PJ, Pajevic S (2007). "Spectral decomposition of a 4th-order covariance tensor: applications to diffusion tensor MRI". Signal Processing. 87 (2): 220–236
Diffusion-weighted magnetic resonance imaging
Diffusion-weighted_magnetic_resonance_imaging
Generalization of the product rule in calculus
Stokes' Divergence Generalized Stokes Helmholtz decomposition Multivariable Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative
General_Leibniz_rule
Computer vision algorithm
Corner Detector Differential Morphological Decomposition Based Corner Detector Multi-scale Bilateral Structure Tensor Based Corner Detector Image Alignment
Harris_corner_detector
Integral of sin(x)/x from 0 to infinity
Stokes' Divergence Generalized Stokes Helmholtz decomposition Multivariable Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative
Dirichlet_integral
Topics referred to by the same term
toroidal surface into polygons. Tensor ring decomposition, a fundamental numerical model representing high-dimensional tensors through circular multilinear
Toroidal
Differentiation under the integral sign formula
Stokes' Divergence Generalized Stokes Helmholtz decomposition Multivariable Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative
Leibniz_integral_rule
Mathematical operation
mixed tensor field will then transform using Φ {\displaystyle \Phi } and Φ − 1 {\displaystyle \Phi ^{-1}} according to the tensor product decomposition of
Pullback (differential geometry)
Pullback_(differential_geometry)
\left[{\frac {n}{2}}\right]} , the tensor product multiplicities that appear in the tensor product decomposition U λ ⊗ U μ = ⊕ ν N λ , μ , ν U ν {\displaystyle
Representations of classical Lie groups
Representations_of_classical_Lie_groups
Derivative defined on normed spaces
{\displaystyle f} at x . {\displaystyle x.} Moreover, by definition of the tensor product, we may identify a member of the space L n ( V × V × ⋯ × V , W )
Fréchet_derivative
Hamiltonian formulation of general relativity
four-dimensional version, such as the metric tensor for three-dimensional slices g i j {\displaystyle g_{ij}} and the metric tensor for the full four-dimensional spacetime
ADM_formalism
Coordinate system whose directions vary in space
example, scalars, vectors, or tensors. Mathematical expressions involving these quantities in vector calculus and tensor analysis (such as the gradient
Curvilinear_coordinates
commonly used measure of stress is the Cauchy stress tensor, often called simply the stress tensor or "true stress". However, several alternative measures
Alternative_stress_measures
Instantaneous rate of change of the function
of a material element in a velocity field Structure tensor – Tensor related to gradients Tensor derivative (continuum mechanics) Total derivative – Type
Directional_derivative
Multivariate derivative (mathematics)
the Einstein summation notation is used and the tensor product of the vectors ei and ek is a dyadic tensor of type (2,0)). Overall, this expression equals
Gradient
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
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
Surname or Lastname
French
French : unexplained.English : unexplained.Possibly a respelling of Menter, an unexplained name of German origin.
Surname or Lastname
English
English : patronymic from the personal name Henn(e), a short form of Henry 1, Hayne (see Hain 2), or Hendy.Irish : Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).
Surname or Lastname
English
English : patronymic from the medieval personal name Benne, a pet form of Benedict (see Benn).English : habitational name from a place in Oxfordshire named Benson, from Old English Benesingtūn ‘settlement (Old English tūn) associated with Benesa’, a personal name of obscure origin, perhaps a derivative of Bana meaning ‘slayer’.Jewish (Ashkenazic) : patronymic composed of a pet form of the personal name Beniamin (see Bien, Benjamin) + German Sohn ‘son’.Scandinavian : altered form of such names as Bengtsson, Bendtsen, patronymics from Bengt, Bendt, etc., Scandinavian forms of Benedict.
Surname or Lastname
German
German : variant of Tanner 2.English : from Old French teneor, teneur, tenor, ‘holder of a tenement’, hence an equivalent of Tennant.
Surname or Lastname
English
English : habitational name for someone from Edensor in Derbyshire, which derives its name from the genitive case of the Old English personal name Ēadhūn (see Eden 1) + Old English ofer ‘ridge’.
Surname or Lastname
English
English : unexplained.
Surname or Lastname
English
English : patronymic from a reduced form of the personal name Steven.English : habitational name from a place in Derbyshire, recorded in Domesday Book as Steintune, later as Steineston, from the Old Norse personal name Steinn (meaning ‘stone’) + Old English tūn ‘enclosure’, ‘settlement’.Variant of Steenson 2.
Boy/Male
French
Works in iron.
Boy/Male
Muslim
Winner
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : nickname for a peasant who gave himself airs and graces, from Anglo-Norman French segneur ‘lord’ (Latin senior ‘elder’).English and Dutch : distinguishing nickname for the elder of two bearers of the same personal name (for example, a father and son or two brothers), from Latin senior ‘elder’.
Male
Greek
(ÎœÎντωÏ) Greek name derived from the word menos, MENTOR means "spirit." In mythology, this is the name of the son of Ãlkimos.
Surname or Lastname
English
English : variant of Tennyson.
Surname or Lastname
English
English : variant spelling of Ensor.
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
Surname or Lastname
English
English : variant of Windsor. This is the spelling used for places so named in Devon and Hampshire.Perhaps also an Americanized spelling of German Winzer.
Surname or Lastname
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Surname or Lastname
English
English : probably a variant of Manser.
Boy/Male
Polish Spanish
Surname or Lastname
English
English : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
Boy/Male
Greek
Pearl.
Girl/Female
Tamil
Wife of Lord Shiva, Goddess Parvati
Surname or Lastname
English
English : variant of William, from a central French form in which W is replaced by G.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Moon
Boy/Male
Tamil
Krishiv | கà¯à®°à®¿à®·à¯€à®µÂ
Lord Krishna and Lord Shiva
Girl/Female
Tamil
Admired, Glorious, Excellent
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
A Great Treasure House
Boy/Male
Hindu
Lord Ganesh, Soldier, Many
Boy/Male
Hindu
Arrow
Girl/Female
Hindu, Indian, Marathi, Sanskrit
A Holy River; River in Ayodhya
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
TENSOR DECOMPOSITION
superl.
Apt to give pain; causing grief or pain; delicate; as, a tender subject.
v. t.
To have a care of; to be tender toward; hence, to regard; to esteem; to value.
n.
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.
n.
One in the fourth or final year of his collegiate course at an American college; -- originally called senior sophister; also, one in the last year of the course at a professional schools or at a seminary.
a.
More advanced than another in age; prior in age; elder; hence, more advanced in dignity, rank, or office; superior; as, senior member; senior counsel.
n.
Tension.
a.
Expansive force; the force with which the particles of a body, as a gas, tend to recede from each other and occupy a larger space; elastic force; elasticity; as, the tension of vapor; the tension of air.
v. t.
To offer in payment or satisfaction of a demand, in order to save a penalty or forfeiture; as, to tender the amount of rent or debt.
n.
Any offer or proposal made for acceptance; as, a tender of a loan, of service, or of friendship; a tender of a bid for a contract.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
n.
A muscle that stretches a part, or renders it tense.
n.
A person who sings the tenor, or the instrument that play it.
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
a.
Sensory; as, the sensor nerves.
a.
The force by which a part is pulled when forming part of any system in equilibrium or in motion; as, the tension of a srting supporting a weight equals that weight.
n.
The quality or state of being tense, or strained to stiffness; tension; tenseness.
n.
A machine or frame for stretching cloth by means of hooks, called tenter-hooks, so that it may dry even and square.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
a.
The act of stretching or straining; the state of being stretched or strained to stiffness; the state of being bent strained; as, the tension of the muscles, tension of the larynx.