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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
Algebraic object with geometric applications
a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may
Tensor
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)
Mathematical operation on vector spaces
two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense
Tensor_product
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
Branch of mathematics
algebra concepts find applications in various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket
Multilinear_algebra
Algebra associated to any vector space
manipulations involving the tensor and wedge symbols. This distinction is developed in greater detail in the article on tensor algebras. Here, there is much
Exterior_algebra
Operation that pairs a left and a right R-module into an abelian group
of scalars. For a commutative ring, the tensor product of modules can be iterated to form the tensor algebra of a module, allowing one to define multiplication
Tensor_product_of_modules
Ring that is also a vector space or a module
category of R-algebras. Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for more
Associative_algebra
Associative algebra together with a Lie bracket that satisfies Leibniz's law
enveloping algebras. The construction proceeds by first building the tensor algebra of the underlying vector space of the Lie algebra. The tensor algebra is simply
Poisson_algebra
Concept in mathematics
tensor algebra T ( g ) {\displaystyle T({\mathfrak {g}})} from it. The tensor algebra is a free algebra: it simply contains all possible tensor products
Universal_enveloping_algebra
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
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 product of algebras over a field; itself another algebra
mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the ring
Tensor_product_of_algebras
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 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
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
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
"Smallest" commutative algebra that contains a vector space
symmetric algebra. As the symmetric algebra of a vector space is a quotient of the tensor algebra, an element of the symmetric algebra is not a tensor, and
Symmetric_algebra
Algebra based on a vector space with a quadratic form
diagonalization. The free algebra generated by V may be written as the tensor algebra ⨁n≥0 V ⊗ ⋯ ⊗ V, that is, the direct sum of the tensor product of n copies
Clifford_algebra
Free object in the category of associative algebras
category of R-algebras to the category of sets. Free algebras over division rings are free ideal rings. Cofree coalgebra Tensor algebra Free object Noncommutative
Free_algebra
Algebraic operation on coordinate vectors
(single-) dot product between a tensor of order n {\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle
Dot_product
multilinear algebra. Ricci calculus The earliest foundation of tensor theory – tensor index notation. Order of a tensor The components of a tensor with respect
Glossary_of_tensor_theory
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
Algebra used in certain conformal field theories
fusion of primary fields. In the context of modular tensor categories, there is also a Verlinde algebra. It is defined to have a basis of elements [ A ]
Verlinde_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
Structure dual to a unital associative algebra
"internal" tensor product of a tensor algebra. A tensor algebra comes with a tensor product (the internal one); it can also be equipped with a second tensor product
Coalgebra
Software library for LLM inference
Gerganov started work on the GGML library, a C library implementing tensor algebra. Gerganov developed the library with the intention of strict memory
Llama.cpp
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 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
Construction in algebra
Hopf algebra is particularly nice, since the existence of compatible comultiplication, counit, and antipode allows for the construction of tensor products
Hopf_algebra
Operation in algebra and mathematics
There are also algebras over the monads for the alternating tensors Alt ∙ ( − ) {\displaystyle {\text{Alt}}^{\bullet }(-)} and total tensor functors T ∙
Monad_(category_theory)
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
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
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
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
Second order tensor in vector algebra
specifically multilinear algebra, a dyadic or dyadic tensor is a second-order tensor, written in a notation that fits in with vector algebra. There are numerous
Dyadics
Vector operation
referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with: The dot product (a special case of
Outer_product
*-algebra of bounded operators on a Hilbert space
to be the von Neumann algebra generated by their algebraic tensor product, considered as operators on the Hilbert space tensor product of the Hilbert
Von_Neumann_algebra
Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra Symmetric
Outline_of_linear_algebra
Antisymmetric permutation object acting on tensors
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a
Levi-Civita_symbol
Characterizing property of mathematical constructions
property is used rather than the concrete details. For example, the tensor algebra of a vector space is slightly complicated to construct, but much easier
Universal_property
Concept in machine learning
learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data
Tensor_(machine_learning)
Exterior algebraic map taking tensors from p forms to n-p forms
Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate
Hodge_star_operator
Type of monoidal category
topological quantum field theory, conformal field theory, and quantum algebra. Modular tensor categories were introduced in 1989 by the physicists Greg Moore
Modular_tensor_category
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
Class of mathematical software
(indicial) tensor manipulation, ctensor for component-defined tensors, and atensor for algebraic tensor manipulation. Tensor is an R package for basic tensor operations
Tensor_software
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
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
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
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)
Algebraic structure in homological algebra
homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often
Differential_graded_algebra
Algebraic structure in mathematics
enveloping algebra of a Lie algebra, with generators a basis of the Lie algebra and relations of the form XY – YX – [X, Y] = 0. The tensor algebra, symmetric
Quadratic_algebra
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
Type of derivative in differential geometry
differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field
Lie_derivative
Structurable algebra Supercommutative algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann algebra Weyl algebra
List_of_algebras
Algebraic generalization of the derivative
-derivation on the algebra of differentiable functions on a differentiable manifold; more generally it is a derivation on the tensor algebra of a manifold
Derivation (differential algebra)
Derivation_(differential_algebra)
Second-rank tensor in quantum chromodynamics
In theoretical particle physics, the gluon field strength tensor is a second-order tensor field characterizing the gluon interaction between quarks. The
Gluon_field_strength_tensor
Expression that may be integrated over a region
p} . When the exterior algebra is viewed as a quotient of the tensor algebra, the exterior product corresponds to the tensor product (modulo the equivalence
Differential_form
theorem still holds for Leibniz algebras and that a weaker version of the Levi–Malcev theorem also holds. The tensor module, T ( V ) = ⨁ i = 1 ∞ V ⊗ i
Leibniz_algebra
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
geometry and modern tensor calculus, particularly in formulations of gauge theory and topological field models. In linear algebra, the n × n {\displaystyle
Kronecker_delta
Branch of mathematics that studies algebraic structures
Group ring Localization of a ring Tensor algebra Symmetric algebra, Exterior algebra, Clifford algebra Free algebra Completion (ring theory) Field (mathematics)
List of abstract algebra topics
List_of_abstract_algebra_topics
Ways of writing certain laws of physics
t^{2}}-\nabla ^{2}.} The signs in the following tensor analysis depend on the convention used for the metric tensor. The convention used here is (+ − − −), corresponding
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Mapping from p forms to p-1 forms
Method in algebraic topology Inner product – Vector space with generalized dot productPages displaying short descriptions of redirect targets Tensor contraction –
Interior_product
Algebraic structure in linear algebra
commute with the tensor product ⊗, much the same way as with the tensor product of two vector spaces introduced in the above section on tensor products. In
Vector_space
Topological space that locally resembles Euclidean space
Euclidean space, an algebraic variety is glued together from affine algebraic varieties, which are zero sets of polynomials over algebraically closed fields
Manifold
Shorthand notation for tensor operations
the multiplication. Given a tensor, one can raise an index or lower an index by contracting the tensor with the metric tensor, g μ ν {\displaystyle g_{\mu
Einstein_notation
Vector behavior under coordinate changes
In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Algebraic structure used in analysis
{g}})\oplus \cdots } be the tensor algebra on g {\displaystyle {\mathfrak {g}}} , also called the free associative algebra on the vector space g {\displaystyle
Lie_algebra
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
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
Concept in stochastic analysis
tensor algebra (more precisely: in the free nilpotent group embedded in the free tensor algebra), which this section now briefly recalls. The tensor powers
Rough_path
Type of physical quantity
spacetime Tensor – Algebraic object with geometric applications Tensor density – Generalization of tensor fields Tensor field – Assignment of a tensor continuously
Pseudotensor
Unified field theory
Kaluza originally provided a stress–energy tensor for his theory, and Thiry included a stress–energy tensor in his thesis. But as described by Gonner,
Kaluza–Klein_theory
Set of vectors used to define coordinates
program Coordinate system Change of basis – Coordinate change in linear algebra Frame of a vector space – Similar to the basis of a vector space, but not
Basis_(linear_algebra)
Writing Lie algebra sets as matrices
representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms
Lie_algebra_representation
Differential form of degree one or section of a cotangent bundle
transform of a real-space lattice, important in solid-state physics Tensor – Algebraic object with geometric applications "2 Introducing Differential Geometry‣
One-form
Operation in Hamiltonian mechanics
well: it occurs in the theory of Lie algebras, where the tensor algebra of a Lie algebra forms a Poisson algebra; a detailed construction of how this
Poisson_bracket
Representation of a tensor in Euclidean space
linear algebra, 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
Cartesian_tensor
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
Isomorphism between the tangent and cotangent bundles of a manifold
index of an ( r , s ) {\displaystyle (r,s)} tensor gives a ( r − 1 , s + 1 ) {\displaystyle (r-1,s+1)} tensor, while raising an index gives a ( r + 1 ,
Musical_isomorphism
Clifford algebra in 4 dimensions
six-dimensional representation space of the tensor (1, 0) ⊕ (0, 1)-representation of the Lorentz algebra inside C l 1 , 3 ( R ) {\displaystyle {\mathcal
Dirac_algebra
Non-tensorial representation of the spin group
orthogonal Lie algebras are distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations
Spinor
Differential algebra
{\text{ for }}v,u\in V)\!),} where T ( V ) {\displaystyle T(V)} is the tensor algebra on V {\displaystyle V} , and the notation ( ( ) ) {\displaystyle (\
Weyl_algebra
Tensor algebra, Tensor analysis, Tensor calculus, Tensor theory the study and use of tensors, which are generalizations of vectors. A tensor algebra is
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
Array of numbers
"two-by-three matrix", a 2 × 3 matrix, or a matrix of dimension 2 × 3. In linear algebra, matrices are used as linear maps. In geometry, matrices are used for geometric
Matrix_(mathematics)
Conserved physical quantity; rotational analogue of linear momentum
as an anti-symmetric second order tensor, with components ωij. The relation between the two anti-symmetric tensors is given by the moment of inertia which
Angular_momentum
matter in fluid mechanics and continuum mechanics. Elementary vector and tensor algebra in curvilinear coordinates is used in some of the older scientific literature
Tensors in curvilinear coordinates
Tensors_in_curvilinear_coordinates
Continuous surjection satisfying a local triviality condition
property is formally captured in the notion of dependent type. Affine bundle Algebra bundle Characteristic class Covering map Equivariant bundle Fibered manifold
Fiber_bundle
Electromagnetism in general relativity
inverse of the metric tensor g α β {\displaystyle g_{\alpha \beta }} , and g {\displaystyle g} is the determinant of the metric tensor. Notice that A α {\displaystyle
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Sum of elements on the main diagonal
models without the need for tensor notation.[non-primary source needed] Trace of a tensor with respect to a metric tensor Characteristic function Field
Trace_(linear_algebra)
Multi particle state space
vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H (see symmetric algebra and exterior algebra respectively). A general state
Fock_space
Method for specifying point positions
Clement (1912). An Introduction to Algebraical Geometry. Clarendon. Hodge, W.V.D.; D. Pedoe (1994) [1947]. Methods of Algebraic Geometry, Volume I (Book II)
Coordinate_system
Portion of a solid that lies between two parallel planes cutting the solid
Stanislaw Lem's short-story collection The Cyberiad, the poem Love and tensor algebra claims that "every frustum longs to be a cone". Buckets and typical
Frustum
Mathematical Concept
mathematics, Voigt notation or Voigt form in multilinear algebra is a way to represent a symmetric tensor by reducing its order. There are a few variants and
Voigt_notation
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
Tensor algebra arising in functional analysis
In mathematics, a Borchers algebra, Borchers–Uhlmann algebra, or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions
Borchers_algebra
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
Theory of gravitation as curved spacetime
stress–energy tensor, which includes both energy and momentum densities as well as stress: pressure and shear. Using the equivalence principle, this tensor is readily
General_relativity
TENSOR ALGEBRA
TENSOR ALGEBRA
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.
Boy/Male
French
Works in iron.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
Surname or Lastname
English
English : variant of Tennyson.
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
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’.
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 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.
Surname or Lastname
English
English : probably a variant of Manser.
Boy/Male
Muslim
Winner
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 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 : 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 : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Surname or Lastname
English
English : variant spelling of Ensor.
Surname or Lastname
English
English : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
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’.
Boy/Male
Polish Spanish
Surname or Lastname
English
English : unexplained.
TENSOR ALGEBRA
TENSOR ALGEBRA
Boy/Male
Tamil
Related to elf
Surname or Lastname
Jewish (Ashkenazic)
Jewish (Ashkenazic) : metonymic occupational name for a refiner, from Yiddish test ‘crucible’, ‘melting pot’.English : nickname for someone with a large or otherwise remarkable head, from Old French teste ‘head’.
Boy/Male
German
Army man; soldier. Famous Bearer: romantic actor Armand Assante.
Girl/Female
Spanish American Latin Persian
Rich.
Boy/Male
Bengali, Hindu, Indian, Kannada, Tamil, Telugu
Chera Prince who Wrote Tamil Masterpiece Silappadhikaram
Girl/Female
Hindu
Goddess Sita (Daughter of king Janak)
Girl/Female
Hindu
Driving, Falcon, Long-legged, Spider
Biblical
falsehood of a song; rejoicing
Girl/Female
Muslim/Islamic
Name of prophet Muhammad's (pbuh) daughter
Male
Czechoslovakian
, treasure watcher; or, the real knight, or, leader of the knights.
TENSOR ALGEBRA
TENSOR ALGEBRA
TENSOR ALGEBRA
TENSOR ALGEBRA
TENSOR ALGEBRA
n.
A person who sings the tenor, or the instrument that play it.
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.
superl.
Apt to give pain; causing grief or pain; delicate; as, a tender subject.
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.
n.
The quality or state of being tense, or strained to stiffness; tension; tenseness.
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 have a care of; to be tender toward; hence, to regard; to esteem; to value.
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.
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.
a.
Sensory; as, the sensor nerves.
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.
A machine or frame for stretching cloth by means of hooks, called tenter-hooks, so that it may dry even and square.
n.
A muscle that stretches a part, or renders it tense.
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.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
n.
Tension.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
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.