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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 wave functions
a chain of N tensors of order 2 or 3, which gives us a polynomial number of parameters. Tensor Tensor diagrams Tensor contraction Tensor Processing Unit
Tensor_network
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
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
The Tensor Contraction Engine (TCE) is a compiler for a domain-specific language that allows chemists to specify the computation in a high-level Mathematica-style
Tensor_Contraction_Engine
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
Measure of the curvature of a pseudo-Riemannian manifold
Riemann tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction on any
Weyl_tensor
Mathematical notation for tensors and spinors
the trace of a tensor t = t a b c {\displaystyle t=t_{ab}{}^{c}} over its last two slots. This manner of representing tensor contractions by repeated indices
Abstract_index_notation
Topics referred to by the same term
routing Contraction mapping, a type of function on a metric space Edge contraction or vertex contraction, graph operations used in graph theory Tensor contraction
Contraction
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
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
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
Branch of mathematics
Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor contraction Symmetric algebra, Symmetric power Symmetric tensor Mixed tensor Pandey, Divyanshu;
Multilinear_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
Muscle of the middle ear
tensor tympani muscle in the middle ear as part of the startle response to some sounds. This lowered reflex threshold for tensor tympani contraction is
Tensor_tympani_muscle
Specification of a derivative along a tangent vector of a manifold
to arbitrary tensor fields, in a unique way that ensures compatibility with the tensor product and trace operations (tensor contraction). Given a point
Covariant_derivative
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
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
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
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
Tensor equal to the negative of any of its transpositions
the contraction with a tensor B that is symmetric on indices i {\displaystyle i} and j {\displaystyle j} is identically 0. For a general tensor U with
Antisymmetric_tensor
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
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
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
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)
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
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
Mapping from p forms to p-1 forms
dot productPages displaying short descriptions of redirect targets Tensor contraction – Operation in mathematics Tu, Sec 20.5. There is another formula
Interior_product
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)
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
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
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
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
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
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
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
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
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 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
Contraction of length in the direction of propagation in Minkowski space
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in
Length_contraction
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
Exterior algebraic map taking tensors from p forms to n-p forms
can apply this expression to any tensor α {\displaystyle \alpha } , the result is antisymmetric, since contraction with the completely anti-symmetric
Hodge_star_operator
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
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
Topological space that locally resembles Euclidean space
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Manifold
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
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
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
Theory of interwoven space and time by Albert Einstein
time measured between two events by observers in motion differ § Length contraction – distances between two events by observers in motion differ The § Lorentz
Special_relativity
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
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
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
Equation in which all expressions are tensors
is one in which all expressions are tensors. The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant
Manifest_covariance
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
Branch of mathematics
where N J {\displaystyle N_{J}} is a tensor of type (2, 1) related to J {\displaystyle J} , called the Nijenhuis tensor (or sometimes the torsion). An almost
Differential_geometry
Mathematical Concept
notation is as follows: Write down the second order tensor in matrix form (in the example, the stress tensor) Strike out the diagonal Continue on the third
Voigt_notation
Vector behavior under coordinate changes
consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Moment of inertia of diff geometric shapes
\cdot \mathbf {n} \equiv n_{i}I_{ij}n_{j}\,,} where the dots indicate tensor contraction and the Einstein summation convention is used. In the above table
List_of_moments_of_inertia
Pictorial computational technique in quantum chemistry
over the inner product, also known in this context as a contraction (cf. tensor contraction): ∑ m ⟨ j , m | j , m ⟩ = 2 j + 1 {\displaystyle \sum _{m}\langle
Angular momentum diagrams (quantum mechanics)
Angular_momentum_diagrams_(quantum_mechanics)
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
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
Array of numbers describing a metric connection
corresponding gravitational potential being the metric tensor. When the coordinate system and the metric tensor share some symmetry, many of the Γijk are zero
Christoffel_symbols
Five-dimensional metric
Riemann–Christoffel curvature tensor). Its contraction with itself is the Kaluza–Klein–Ricci tensor, a generalization of the Ricci tensor. Its contraction with the Kaluza–Klein
Kaluza–Klein_metric
Matrix operation which flips a matrix over its diagonal
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Transpose
Method for specifying point positions
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Coordinate_system
Differential form of degree one or section of a cotangent bundle
one coordinate system to another. Thus a one-form is an order 1 covariant tensor field. The most basic non-trivial differential one-form is the "change in
One-form
Array of numbers
multiplication can be defined with entries objects of a category equipped with a "tensor product" similar to multiplication in a ring, having coproducts similar
Matrix_(mathematics)
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
Differential form
absolute value of the determinant of the matrix representation of the metric tensor on the manifold. The volume form is denoted variously by ω = v o l n = ε
Volume_form
Branch of physics which studies the behavior of materials modeled as continuous media
stress tensor, and ρ 0 {\displaystyle \rho _{0}} is the mass density in the reference configuration. The first Piola-Kirchhoff stress tensor is related
Continuum_mechanics
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
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
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
Expression that may be integrated over a region
covariant tensor field of rank k {\displaystyle k} . The differential forms on M {\displaystyle M} are in one-to-one correspondence with such tensor fields
Differential_form
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
Punctuation mark with two dots (:)
also sometimes used to indicate a tensor contraction involving two indices, and a double colon (::) for a contraction over four indices. A colon is also
Colon_(punctuation)
Topics referred to by the same term
Look up tense in Wiktionary, the free dictionary. Tense may refer to: Tense, a state of muscle contraction Grammatical tense, a property of verbs indicating
Tense
Property of a mathematical space
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Dimension
formal adjoint, V is the Schouten tensor, J is the trace of the Schouten tensor, and the dot denotes tensor contraction on either index. Here Q is the scalar
Paneitz_operator
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
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
Continuous surjection satisfying a local triviality condition
notation Tensor definitions Tensor (intrinsic definition) Tensor field Tensor density Tensors in curvilinear coordinates Mixed tensor Antisymmetric tensor Symmetric
Fiber_bundle
Non-tensorial representation of the spin group
distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations are integer
Spinor
Straight path on a curved surface or a Riemannian manifold
and real trees. In a Riemannian manifold M {\displaystyle M} with metric tensor g {\displaystyle g} , the length L {\displaystyle L} of a continuously differentiable
Geodesic
Sum of elements on the main diagonal
setting of superalgebras. The operation of tensor contraction generalizes the trace to arbitrary tensors. Gomme and Klein (2011) define a matrix trace
Trace_(linear_algebra)
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
Array of processing elements specialized for parallelizable workloads
consist of matrix multiplications, convolutions, or, in general, tensor contractions. As such, spatial architectures are often used in AI accelerators
Spatial_architecture
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
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
that is 0 whenever arguments are linearly dependent Antisymmetric tensor – Tensor equal to the negative of any of its transpositions Hazewinkel (1990)
Symmetrization
Small set of grammatically distinctive verbs of English
go show that to allows negation. Inversion, contraction of not, and rebuttal would only apply to tensed forms, and to is argued to have none. Although
English_auxiliary_verbs
Type of polynomial
the vectors [1 x], [1 y], etc. The general form can be written as a tensor contraction: f ( x ) = ∑ i 1 = 0 1 ∑ i 2 = 0 1 ⋯ ∑ i n = 0 1 a i 1 i 2 ⋯ i n x
Multilinear_polynomial
implements the computation of the Riemann curvature tensor and associated objects (Ricci tensor, Weyl tensor). SageManifolds can also deal with generic affine
Sage_Manifolds
Function that is invariant under all permutations of its variables
functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric k {\displaystyle k} -tensors on a vector
Symmetric_function
Four-vector analogue of the gradient operation
In GR, one must use the more general metric tensor g α β {\displaystyle g^{\alpha \beta }} and the tensor covariant derivative ∇ μ = ; μ {\displaystyle
Four-gradient
Topics referred to by the same term
of how individuals connect with society Tensor contraction, in mathematics and physics, an operation on tensors This disambiguation page lists articles
Contract_(disambiguation)
Theoretical Physicist
theoretical physicist who specializes in quantum information science and quantum tensor networks. He is Ikerbasque Research Professor at the Donostia International
Román_Orús
Theorem in calculus
i_{q}\cdots i_{n}}n_{i_{q}}\,\mathrm {d} S.} where on each side, tensor contraction occurs for at least one index. This form of the theorem is still in
Divergence_theorem
Affine connection on the tangent bundle of a manifold
components of a contravariant vector. This discovery was the real beginning of tensor analysis. In 1906, L. E. J. Brouwer was the first mathematician to consider
Levi-Civita_connection
Set of vectors used to define coordinates
of redirect targets Spherical basis – Basis used to express spherical tensors Brown, William A. (1991). Matrices and vector spaces. New York: M. Dekker
Basis_(linear_algebra)
TENSOR CONTRACTION
TENSOR CONTRACTION
Surname or Lastname
English
English : variant of Tennyson.
Male
Greek
(ÎœÎντωÏ) Greek name derived from the word menos, MENTOR means "spirit." In mythology, this is the name of the son of Ãlkimos.
Boy/Male
French
Works in iron.
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
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
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 of Windsor. This is the spelling used for places so named in Devon and Hampshire.Perhaps also an Americanized spelling of German Winzer.
Boy/Male
Polish Spanish
Surname or Lastname
English
English : variant spelling of Ensor.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
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 : probably a variant of Manser.
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 : 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 : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
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
French
French : unexplained.English : unexplained.Possibly a respelling of Menter, an unexplained name of German origin.
Boy/Male
Muslim
Winner
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
TENSOR CONTRACTION
TENSOR CONTRACTION
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TENSOR CONTRACTION
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
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.
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.
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.
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
n.
A muscle that stretches a part, or renders it tense.
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.
v. t.
To have a care of; to be tender toward; hence, to regard; to esteem; to value.
n.
Tension.
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.
n.
A person who sings the tenor, or the instrument that play it.
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.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
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.
superl.
Apt to give pain; causing grief or pain; delicate; as, a tender subject.