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Mathematical operation on vector spaces
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 of
Tensor_product
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Operation that pairs a left and a right R-module into an abelian group
In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms
Tensor_product_of_modules
Ring produced from two fields
In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the
Tensor_product_of_fields
Mathematical operation on matrices
product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product
Kronecker_product
Operation in graph theory
In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices
Tensor_product_of_graphs
Tensor product of algebras over a field; itself another algebra
In 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
Tensor_product_of_algebras
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 vector algebra
mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There
Dyadics
Tensor product constructions for topological vector spaces
topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well-behaved theory of tensor products (see
Topological_tensor_product
differential graded algebra A over a commutative ring R, the derived tensor product functor is − ⊗ A L − : D ( M A ) × D ( A M ) → D ( R M ) {\displaystyle
Derived_tensor_product
Tensor product space endowed with a special inner product
analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert
Tensor product of Hilbert spaces
Tensor_product_of_Hilbert_spaces
Topics referred to by the same term
Tensor product of Hilbert spaces, endowed with a special inner product as to remain a Hilbert space Other topological tensor products Tensor product of
Tensor product (disambiguation)
Tensor_product_(disambiguation)
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)
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
Universal construction in multilinear algebra
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
Mathematical form
have a tensor product. Other kinds of products in linear algebra include: Hadamard product Kronecker product The product of tensors: Wedge product or exterior
Product_(mathematics)
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
projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely
Projective_tensor_product
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
injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the underlying
Injective_tensor_product
Vector operation
The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with:
Outer_product
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
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
Algebra associated to any vector space
}_{i_{r+p}}.} The components of this tensor are precisely the skew part of the components of the tensor product s ⊗ t, denoted by square brackets on the
Exterior_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
Mathematical group that can be generated as the set of powers of a single element
the group of units of the ring Z, which is ({−1, +1}, ×) ≅ C2. The tensor product Z/mZ ⊗ Z/nZ can be shown to be isomorphic to Z / gcd(m, n)Z. So we can
Cyclic_group
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
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
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)
*-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
Algebraic structure in linear algebra
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 general
Vector_space
Projective tensor product Tensor product of Hilbert spaces – Tensor product space endowed with a special inner product Topological tensor product – Tensor product
Inductive_tensor_product
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)
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
Combination of pointed topological spaces
smash product as a kind of tensor product in an appropriate category of pointed spaces. Adjoint functors make the analogy between the tensor product and
Smash_product
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
Algebraic operation on coordinate vectors
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 n+m-2} (more generally
Dot_product
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
Category admitting tensor products
which ensure that all the relevant diagrams commute. The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal
Monoidal_category
Topological vector spaces
completion of the injective tensor product (which in this case is the identical to the completion of the projective tensor product). Tempered distributions
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
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)
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
Basic circuit in quantum computing
. The tensor product (or Kronecker product) is used to combine quantum states. The combined state for a qubit register is the tensor product of the constituent
Quantum_logic_gate
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
Type of vector space in math
identification of operators with tensor product spaces generalizes to other tensor norms. For example, the injective tensor product H 1 ⊗ ^ ε H 2 {\displaystyle
Hilbert_space
Key concept in higher-order singular value decomposition of functions
In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition
Tensor product model transformation
Tensor_product_model_transformation
A tensor product network, in artificial neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable
Tensor_product_network
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
Normed vector space that is complete
algebraic tensor product X ⊗ Y {\displaystyle X\otimes Y} equipped with the projective tensor norm, and similarly for the injective tensor product X ⊗ ^ ε
Banach_space
Process in linear algebra
refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has numerous applications in quantum information
Schmidt_decomposition
Topic in mathematics
subscript, R {\displaystyle \mathbb {R} } , on the tensor product indicates that the tensor product is taken over the real numbers (since V {\displaystyle
Complexification
Algebra based on a vector space with a quadratic form
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 of V over all n. Therefore
Clifford_algebra
Binary operation on graphs
below for the number of edges in a product also may fail when including self-loops. For example, the tensor product of a single vertex self-loop with itself
Graph_product
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
by coherent isomorphisms. Introduced by Gray, a Gray tensor product is a replacement of a product of 2-categories that is more convenient for higher category
3-category
Mathematical notation for tensors and spinors
between tensor factors of type V {\displaystyle V} and those of type V ∗ {\displaystyle V^{*}} . A general homogeneous tensor is an element of a tensor product
Abstract_index_notation
Coefficients in angular momentum eigenstates of quantum systems
coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation
Clebsch–Gordan_coefficients
Operation in graph theory
been used for Cartesian products of graphs, but is now more commonly used for another construction known as the tensor product of graphs. The square symbol
Cartesian_product_of_graphs
Algebraic structure used in theoretical physics
ungraded tensor product (except that the result is graded). However, in general, the super tensor product is distinct from the tensor product of A {\displaystyle
Superalgebra
Notation for quantum states
)}\,.} Two Hilbert spaces V and W may form a third space V ⊗ W by a tensor product. In quantum mechanics, this is used for describing composite systems
Bra–ket_notation
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
Mathematical operation on vectors in 3D space
cross product can be seen as the (1,2)-tensor (a mixed tensor, specifically a bilinear map) obtained from the 3-dimensional volume form, a (0,3)-tensor, by
Cross_product
Belgian mathematician
Fourier–Deligne transform Deligne cohomology Deligne motive Deligne tensor product of abelian categories (denoted ⊠ {\displaystyle \boxtimes } ) Deligne's
Pierre_Deligne
Construction in homological algebra
f 1 = ⋯ = f r = 0 {\displaystyle f_{1}=\cdots =f_{r}=0} . It is the tensor product of the r many Koszul complexes for f i = 0 {\displaystyle f_{i}=0}
Koszul_complex
Mathematical operation in linear algebra
Kronecker product or tensor product, the generalization to any size of the preceding Khatri–Rao product and face-splitting product Outer product, also called
Matrix_multiplication
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
Map from multiple vectors to an underlying field of scalars, linear in each argument
a k {\displaystyle k} -tensor f ∈ T k ( V ) {\displaystyle f\in {\mathcal {T}}^{k}(V)} and an ℓ {\displaystyle \ell } -tensor g ∈ T ℓ ( V ) {\displaystyle
Multilinear_form
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
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
Index of articles associated with the same name
{\displaystyle W} are vector spaces, their tensor product v ⊗ w {\displaystyle v\otimes w} belongs to the tensor product V ⊗ W {\displaystyle V\otimes W} of
Vector_multiplication
Examples of tensor representations: Not all irreducible representations of G L ( n , C ) {\displaystyle GL(n,\mathbb {C} )} are tensor representations
Representations of classical Lie groups
Representations_of_classical_Lie_groups
Representations of finite groups, particularly on vector spaces
distinguished. The first case is a representation of the group product into the tensor product of the corresponding representation spaces. The second case
Representation theory of finite groups
Representation_theory_of_finite_groups
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
Branch of mathematics
various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning
Multilinear_algebra
of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory
Glossary_of_tensor_theory
Vector differential operator
being a tensor. The tensor derivative of a vector field v {\displaystyle \mathbf {v} } (in three dimensions) is a 9-term second-rank tensor – that is
Del
Defines a notion of parallel transport on a bundle
subspaces of the tensor power, S k E , Λ k E ⊂ E ⊗ k {\displaystyle S^{k}E,\Lambda ^{k}E\subset E^{\otimes k}} , the definition of the tensor product connection
Connection_(vector_bundle)
Generalization of the Cartesian product
{\displaystyle \mathbb {R} ^{n}.} The direct product for modules (not to be confused with the tensor product) is very similar to the one that is defined
Direct_product
Exterior algebraic map taking tensors from p forms to n-p forms
space L ( V , V ) {\displaystyle L(V,V)} is naturally isomorphic to the tensor product V ∗ ⊗ V ≅ V ⊗ V {\displaystyle V^{*}\!\!\otimes V\cong V\otimes V}
Hodge_star_operator
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
Mathematical description of quantum state
studied separately. Under such Hamiltonians, any tensor product state evolves into another tensor product state, which essentially means any unentangled
Wave_function
Concept in mathematical category theory
tensor product is the set theoretic cartesian product, and any singleton can be fixed as the unit object. The category of groups. The tensor product is
Symmetric_monoidal_category
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
Tensor product decomposition rules in representation theory
fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations
Fusion_rules
Value determined from a polyhedron
structure as a tensor gives the Dehn invariant additional properties that are geometrically meaningful. In particular, it has a tensor rank, the minimum
Dehn_invariant
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
Multi particle state space
particles are bosons, the n-particle states are vectors in a symmetrized tensor product of n single-particle Hilbert spaces H. If the identical particles are
Fock_space
Algebraic structure with addition and multiplication
functor.) Let A, B be algebras over a commutative ring R. Then the tensor product of R-modules A ⊗ R B {\displaystyle A\otimes _{R}B} is an R-algebra
Ring_(mathematics)
Theorem in category theory
equivalent to a strict monoidal category. In a monoidal category, the tensor product is associative and unital only up to the natural isomorphisms given
Mac_Lane's_coherence_theorem
Mathematical description of spacetime used in relativity
provide a basis for the cotangent space at p. The tensor product (denoted by the symbol ⊗) yields a tensor field of type (0, 2), i.e. the type that expects
Minkowski_spacetime
Binary operation in graph theory
two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs. An example of a strong product is the king's
Strong_product_of_graphs
category in exactly two ways: with the usual categorical product and with the funny tensor product. Given two categories C {\displaystyle C} and D {\displaystyle
Premonoidal_category
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
List of concrete topologies and topological spaces
topology Inductive tensor product Injective tensor product Projective tensor product Tensor product of Hilbert spaces Topological tensor product Émery topology
List_of_topologies
Relates the homology of two objects to the homology of their product
X\times Y} . In the simplest possible case the relationship is that of a tensor product, but for applications it is very often necessary to apply certain tools
Künneth_theorem
Topics referred to by the same term
Dot product Cross product Seven-dimensional cross product Triple product, in vector calculus Tensor product Product topology Cap product Cup product Slant
Product
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. For larger
Kronecker_delta
Category whose objects are rings and whose morphisms are ring homomorphisms
of rings is a symmetric monoidal category with the tensor product of rings ⊗Z as the monoidal product and the ring of integers Z as the unit object. It
Category_of_rings
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 PRODUCT
TENSOR PRODUCT
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
English
English : probably a variant of Manser.
Surname or Lastname
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
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 : unexplained.
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’.
Boy/Male
French
Works in iron.
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
Surname or Lastname
English
English : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
Surname or Lastname
English
English : variant of Tennyson.
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 : variant spelling of Ensor.
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 : 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 : 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.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
Boy/Male
Muslim
Winner
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.
TENSOR PRODUCT
TENSOR PRODUCT
Girl/Female
African, Arabic, Australian, Indian, Muslim, Sindhi, Swahili
Ease; Prosperous; Convenience
Girl/Female
Armenian, Australian, Indonesian
Kind One; From Armenia
Girl/Female
Greek English
Bee.
Boy/Male
Irish
Irish form of John meaning “â€God’s gracious gift.â€â€ Shane is a very popular variant of the name in Northern Ireland in memory of Shane O’Neill whose forces won notable victories over the armies of Queen Elizabeth 1st in the sixteenth century.
Boy/Male
Australian, French, German, Latin, Portuguese, Shakespearean, Spanish
Dark; Similar to Adrian; The Adriatic Sea; From Hadria
Girl/Female
Greek Russian
Light.
Female
Scottish
Variant spelling of Scottish Arabella, ARABELA means "lovable."
Girl/Female
Tamil
Devangana | தேவாஂகநா
Celestial maiden
Boy/Male
Arabic, Muslim
Arabic Form of Jacob
Girl/Female
Muslim/Islamic
A daughter of Ajlan; She was a narrator of Hadith
TENSOR PRODUCT
TENSOR PRODUCT
TENSOR PRODUCT
TENSOR PRODUCT
TENSOR PRODUCT
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
n.
A machine or frame for stretching cloth by means of hooks, called tenter-hooks, so that it may dry even and square.
n.
The quality or state of being tense, or strained to stiffness; tension; tenseness.
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.
A muscle that stretches a part, or renders it tense.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
a.
Sensory; as, the sensor nerves.
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.
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.
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.
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.
Tension.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
superl.
Apt to give pain; causing grief or pain; delicate; as, a tender subject.
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.
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.
n.
A person who sings the tenor, or the instrument that play it.
v. t.
To have a care of; to be tender toward; hence, to regard; to esteem; to value.