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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
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
Concept in mathematics
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
Structure defining distance on a manifold
section of the tensor product bundle E* ⊗ E*. The metric tensor gives a natural isomorphism from the tangent bundle to the cotangent bundle, sometimes called
Metric_tensor
Mathematical parametrization of vector spaces by another space
F is a vector bundle E ⊕ F over X whose fiber over x is the direct sum Ex ⊕ Fx of the vector spaces Ex and Fx. The tensor product bundle E ⊗ F is defined
Vector_bundle
Operation that pairs a left and a right R-module into an abelian group
example, one can define a tensor field on a smooth manifold M as a (global or local) section of the tensor product (called tensor bundle) ( T M ) ⊗ p ⊗ O ( T
Tensor_product_of_modules
Defines a notion of parallel transport on a bundle
the dual vector bundle E ∗ {\displaystyle E^{*}} , tensor powers E ⊗ k {\displaystyle E^{\otimes k}} , symmetric and antisymmetric tensor powers S k E
Connection_(vector_bundle)
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
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
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
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
Isomorphism between the tangent and cotangent bundles of a manifold
vector bundle endowed with a bundle metric and its dual. Given a (0, 2) tensor X = Xij ei ⊗ ej, we define the trace of X through the metric tensor g by
Musical_isomorphism
Mathematical operation on vector bundles
product. The Hom bundle H o m ( E 1 , E 2 ) {\displaystyle \mathrm {Hom} (E_{1},E_{2})} of two vector bundles is canonically isomorphic to the tensor
Dual_bundle
Topics referred to by the same term
the product is not a field) "Categorified" concepts, applied "pointwise" on objects and morphisms: Tensor product of vector bundles Tensor product of sheaves
Tensor product (disambiguation)
Tensor_product_(disambiguation)
of a metric tensor can be extended to an arbitrary vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or
Bundle_metric
p is a smooth section of the tensor product bundle of E with Λp(T ∗M), the p-th exterior power of the cotangent bundle of M. The space of such forms
Vector-valued differential form
Vector-valued_differential_form
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
Second-rank tensor in quantum chromodynamics
strength tensor is a rank-2 tensor field on the spacetime with values in the adjoint bundle of the chromodynamical SU(3) gauge group (see vector bundle for
Gluon_field_strength_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 operation
(also known as a tensor – not to be confused with a tensor field – of rank (0, s), where s is the number of factors of W in the product). Then the pullback
Pullback (differential geometry)
Pullback_(differential_geometry)
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
Concept in algebraic geometry
line bundle L is big if and only if it has a positive tensor power which is the tensor product of an ample line bundle A and an effective line bundle B (meaning
Ample_line_bundle
Tensorial object depending on two points in a manifold
{\displaystyle (r,s,r',s')} is defined as a section of the exterior tensor product bundle T s r M ⊠ T s ′ r ′ M {\displaystyle T_{s}^{r}M\boxtimes T_{s'}^{r'}M}
Bitensor
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
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
Continuous surjection satisfying a local triviality condition
and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different
Fiber_bundle
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
Section of a certain line bundle
be made, since the density bundle is the tensor product of the orientation bundle of M and the n-th exterior product bundle of T∗M (see pseudotensor).
Density_on_a_manifold
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
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
Functions in mathematics
{\displaystyle M} and that on N {\displaystyle N} on the tensor product bundle T ∗ M ⊗ u − 1 T N {\displaystyle T^{\ast }M\otimes u^{-1}TN}
Harmonic_function
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
Vector bundle of rank 1
global section, and its tensor powers with any real exponent may be defined and used to 'twist' any vector bundle by tensor product. The same construction
Line_bundle
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
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)
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
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 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
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
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
Type of differentiable manifold
Orthonormal frame bundle Principal bundle Connection (mathematics) G-structure Bishop, Richard L.; Goldberg, Samuel I. (1968), Tensor Analysis on Manifolds
Parallelizable_manifold
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
Manifold upon which it is possible to perform calculus
The tensor bundle is the direct sum of all tensor products of the tangent bundle and the cotangent bundle. Each element of the bundle is a tensor field
Differentiable_manifold
Calculus of vector-valued functions
-fold tensor products of vectors and covectors, respectively. Thus a ( p , q ) {\displaystyle (p,q)} tensor field is a map from a manifold to bundles of
Vector_calculus
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
Construct in differenital geometry
connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the
Metric_connection
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
Principal bundle associated to a vector bundle
In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber
Frame_bundle
Exterior algebraic map taking tensors from p forms to n-p forms
a differential form with values in the canonical line bundle. We compute in terms of tensor index notation with respect to a (not necessarily orthonormal)
Hodge_star_operator
Vector bundle existing over a Grassmannian
tautological bundle is a line bundle, the associated invertible sheaf of sections is O ( − 1 ) {\displaystyle {\mathcal {O}}(-1)} , the tensor inverse (ie
Tautological_bundle
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
Mathematics concept
vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B
Vertical and horizontal bundles
Vertical_and_horizontal_bundles
Function in mathematics
invariants, such as the curvature (see also curvature tensor and curvature form), and torsion tensor. Consider the following problem. Suppose that a tangent
Connection_(mathematics)
Vector bundle of cotangent spaces at every point in a manifold
mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold
Cotangent_bundle
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 of a tensor field, which is a section of some tensor bundle, often consisting of exterior powers of the tangent and cotangent bundles. A ( k , 0
Polyvector_field
Complex vector bundle on a complex manifold
the group of isomorphism classes of holomorphic line bundles with group law given by tensor product and inversion given by dualization. It can be equivalently
Holomorphic_vector_bundle
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
Second-order tensor
of the manifold. The Weyl tensor equals the Riemann curvature tensor minus the Kulkarni–Nomizu product of the Schouten tensor with the metric. In an index
Schouten_tensor
Array of numbers describing a metric connection
cotangent space by the metric tensor. Abstractly, one would say that the manifold has an associated (orthonormal) frame bundle, with each "frame" being a
Christoffel_symbols
Object in differential geometry
The contorsion tensor (or contortion tensor) in differential geometry is the difference between a connection with and without torsion in it. It commonly
Contorsion_tensor
Term in differential geometry
form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry can be considered as a special case
Curvature_form
Non-tensorial representation of the spin group
complex vector bundle on a manifold carries a Spinc structure. A number of Clebsch–Gordan decompositions are possible on the tensor product of one spin representation
Spinor
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
Application of Lagrangian mechanics to field theories
fiber bundle, and the derivatives of the field are understood to be sections of the jet bundle. The above can be generalized for vector fields, tensor fields
Lagrangian_(field_theory)
Relates the homology of a fiber bundle with the homologies of its base and fiber
of the Künneth formula, which computes the cohomology of a product space as a tensor product of the cohomologies of the direct factors. It is a very special
Leray–Hirsch_theorem
Quadratic form related to curvatures of surfaces
In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional
Second_fundamental_form
Expression that may be integrated over a region
algebra is embedded as a subspace of the tensor algebra by means of the alternation map, the tensor product α ⊗ β {\displaystyle \alpha \otimes \beta
Differential_form
Concept in mathematics
O P N ( 1 ) {\displaystyle {\mathcal {O}}_{\mathbf {P} ^{N}}(1)} . Tensor products and the inverses of linearized invertible sheaves are again linearized
Equivariant_sheaf
Operator generalizing the Laplacian in differential geometry
the Levi-Civita connection. The Hessian (tensor) of a function f {\displaystyle f} is the symmetric 2-tensor Hess f ∈ Γ ( T ∗ M ⊗ T ∗ M ) , {\displaystyle
Laplace–Beltrami_operator
Type of sheaf of modules
with respect to tensor product of sheaves of modules. It is the equivalent in algebraic geometry of the topological notion of a line bundle. Due to their
Invertible_sheaf
Construct allowing differentiation of tangent vector fields of manifolds
differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully
Affine_connection
Differential form of degree one or section of a cotangent bundle
cotangent bundle. Equivalently, a one-form on a manifold M {\displaystyle M} is a smooth mapping of the total space of the tangent bundle of M {\displaystyle
One-form
Smooth manifold
words, we have a smooth tensor field J of degree (1, 1) such that J 2 = − 1 {\displaystyle J^{2}=-1} when regarded as a vector bundle isomorphism J : T M
Almost_complex_manifold
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
one grand object called the tensor bundle. A tensor field is then defined as a map from the manifold to the tensor bundle, each point p {\displaystyle
Mathematics of general relativity
Mathematics_of_general_relativity
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
construct Cℓ(V) as a quotient of the tensor algebra of V by the ideal generated by the above relation. Like other tensor operations, this construction can
Clifford_bundle
Smooth manifold with an inner product on each tangent space
\operatorname {tr} } is the trace. The Ricci curvature tensor is a covariant 2-tensor field. The Ricci curvature tensor R i c {\displaystyle Ric} plays a defining
Riemannian_manifold
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
Math/physics concept
E-valued forms, thus regarding it as a differential operator on the tensor product of E with the full exterior algebra of differential forms. Given an
Connection_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
correspond to line bundles of degree 0 on A, so there is a natural group operation on Av given by tensor product of line bundles, which makes it into
Dual_abelian_variety
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
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
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
Most general completion of a commutative square given two morphisms with same codomain
coproduct in a category of algebras over a ring R, is given by the tensor product over R, and Spec is a contravariant functor, the pullback of two affine
Pullback_(category_theory)
connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue of Einstein's
Hermitian Yang–Mills connection
Hermitian_Yang–Mills_connection
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
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
the n-th tensor product Kn of the canonical bundle K. The 0th graded component R 0 {\displaystyle R_{0}} is sections of the trivial bundle, and is one-dimensional
Canonical_ring
Mathematical construct of fiber bundles
covariant metric tensor gives an isomorphism g : T M → T ∗ M {\displaystyle g\colon TM\to T^{*}M} from the tangent bundle to the cotangent bundle, which is a
Solder_form
Mathematical concept that extends the intuitive idea of gluing in topology
discussion of the way there of constructing tensor fields can be summed up as "once you learn to descend the tangent bundle, for which transitivity is the Jacobian
Descent_(mathematics)
Basis used to express spherical tensors
a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank k {\displaystyle k} is 1. For
Spherical_basis
Straight path on a curved surface or a Riemannian manifold
double tangent bundle TTM into horizontal and vertical bundles: T T M = H ⊕ V . {\displaystyle TTM=H\oplus V.} The double tangent bundle can be visualized
Geodesic
in a K-group, in which vector bundles may be formally combined by addition, subtraction and multiplication (tensor product). The polynomials here are called
Adams_operation
if n = height(m). A dualizing module need not be unique because the tensor product of any dualizing module with a rank 1 projective module is also a dualizing
Dualizing_module
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
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
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
Surname or Lastname
English
English : variant of Tennyson.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
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
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 : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
Surname or Lastname
French
French : unexplained.English : unexplained.Possibly a respelling of Menter, an unexplained name of German origin.
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
Polish Spanish
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
Boy/Male
Bengali, Indian
First Ray of Sun
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 : 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 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 : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Surname or Lastname
English
English : probably a variant of Manser.
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 : 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
Muslim
Winner
Surname or Lastname
English
English : variant spelling of Ensor.
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
Girl/Female
Hindu
Brahmas daughter, Shining
Girl/Female
British, English, Hindu, Indian, Japanese, Norse, Punjabi, Sikh
Pleasing
Boy/Male
German Hungarian Swedish
Powerful ruler.
Girl/Female
Indian
Companion, Celebration
Boy/Male
Arabic, Australian, Biblical
Abraham's Brother; Noise; Tumult
Girl/Female
Hindu, Indian
Bringing Happiness
Boy/Male
Tamil
Interesting, Pleasant
Boy/Male
Hindu
Is associated to Lord Shiva, Durga, Vishnu, Lakshmi
Surname or Lastname
English
English : from a short form of the personal name Alexander.
Girl/Female
Hindu, Indian
Small Bowl
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
TENSOR PRODUCT-BUNDLE
n.
Anything that is produced, whether as the result of generation, growth, labor, or thought, or by the operation of involuntary causes; as, the products of the season, or of the farm; the products of manufactures; the products of the brain.
v. t.
To produce; to bring forward.
imp. & p. p.
of Produce
v. t.
To bring forth, as young, or as a natural product or growth; to give birth to; to bear; to generate; to propagate; to yield; to furnish; as, the earth produces grass; trees produce fruit; the clouds produce rain.
superl.
Adapted to excite feeling or sympathy; expressive of the softer passions; pathetic; as, tender expressions; tender expostulations; a tender strain.
v. t.
To extend; -- applied to a line, surface, or solid; as, to produce a side of a triangle.
n.
A secondary or additional product; something produced, as in the course of a manufacture, in addition to the principal product.
n.
A person who sings the tenor, or the instrument that play it.
n.
agricultural products.
v. t.
To produce; to make.
v. t.
To yield or furnish; to gain; as, money at interest produces an income; capital produces profit.
v. t.
To draw out; to extend; to lengthen; to prolong; as, to produce a man's life to threescore.
n.
That which is produced, brought forth, or yielded; product; yield; proceeds; result of labor, especially of agricultural labors
superl.
Easily impressed, broken, bruised, or injured; not firm or hard; delicate; as, tender plants; tender flesh; tender fruit.
v. t.
To cause to be or to happen; to originate, as an effect or result; to bring about; as, disease produces pain; vice produces misery.
n.
A muscle that stretches a part, or renders it tense.
v. i.
To form a project; to scheme.
n.
Tension.
a.
Sensory; as, the sensor nerves.