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geometry, a field in mathematics, a multivector field, polyvector field of degree k {\displaystyle k} , or k {\displaystyle k} -vector field, on a smooth
Multivector_field
Element of an exterior algebra
In multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra Λ(V) of a vector space V. This
Multivector
of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different versions
Schouten–Nijenhuis_bracket
Infinitesimal calculus on functions defined on a geometric algebra
to a general multivector, called the multivector derivative. Let F {\displaystyle F} be a multivector-valued function of a multivector. The directional
Geometric_calculus
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
Formulations of electromagnetism
{\displaystyle C\ell _{3,0}(\mathbb {R} )} , the field and current are represented by multivectors. The field multivector, known as the Riemann–Silberstein vector
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
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
Mathematical structure in non-Riemannian differential geometry
⋅ , ⋅ ] A {\displaystyle [\cdot ,\cdot ]_{A}} can be extended to multivector fields Γ ( ∧ A ) {\displaystyle \Gamma (\wedge A)} graded symmetric via the
Lie_bialgebroid
Mathematical object that describes the electromagnetic field in spacetime
electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a tensor that describes the electromagnetic field in
Electromagnetic_tensor
Branch of mathematics
respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants
Multilinear_algebra
Algebraic object with geometric applications
tensors, that vary across space in this way, is a tensor field. In some areas, tensor fields are so ubiquitous that they are often simply called "tensors"
Tensor
differential forms on a Poisson manifold form a Gerstenhaber algebra. The multivector fields on a manifold form a Gerstenhaber algebra using the Schouten–Nijenhuis
Gerstenhaber_algebra
Mapping from p forms to p-1 forms
a vector X (which has grade 1), a homogeneous multivector a having grade p, and an arbitrary multivector b, the right interior product satisfies the rule
Interior_product
Algebraic structure designed for geometry
Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric
Geometric_algebra
Theory of gravitation as curved spacetime
including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. John
General_relativity
Mathematical structure in differential geometry
{{\mathfrak {X}}^{p+q-1}}(M)} denotes the Schouten–Nijenhuis bracket on multivector fields. Choosing local coordinates ( U , x i ) {\displaystyle (U,x^{i})}
Poisson_manifold
Specification of a derivative along a tangent vector of a manifold
an introduction to the covariant derivative of a vector field with respect to a vector field, both in a coordinate-free language and using a local coordinate
Covariant_derivative
Type of derivative in differential geometry
change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate
Lie_derivative
}{\partial q^{i}}}} Let f ( x ) {\displaystyle f(\mathbf {x} )} be a scalar field in space. Then f ( x ) = f [ φ ( q 1 , q 2 , q 3 ) ] = f φ ( q 1 , q 2
Tensors in curvilinear coordinates
Tensors_in_curvilinear_coordinates
Algebra of 4D spacetime
conjugation. If g ∈ G 3 {\displaystyle g\in \mathbb {G} _{3}} is an arbitrary multivector and ⟨ g ⟩ j {\displaystyle \langle g\rangle _{j}} projects g {\displaystyle
Algebra_of_physical_space
Operation in mathematics
pointwise to a tensor field, e.g. if T is a (1,1) tensor field on Euclidean space, then in any coordinates, its contraction (a scalar field) U at a point x
Tensor_contraction
Tensor describing energy momentum density in spacetime
stress–energy–momentum tensor or the energy–momentum tensor, is a tensor field quantity that describes the density and flux of energy and momentum at each
Stress–energy_tensor
Non-tensorial representation of the spin group
{\displaystyle H_{2}} is a three-dimensional vector space over the real field. The negative determinant of X {\displaystyle X} is − det X = x 2 + | z
Spinor
Physical quantity that changes sign with improper rotation
terminology to describe the various combinations is provided. For example, a multivector is a summation of k-fold wedge products of various k-values. A k-fold
Pseudovector
Coordinate-free definition of a tensor
tensor field on a manifold, and then doesn't need to make reference to coordinates at all. The same is true in general relativity, of tensor fields describing
Tensor_(intrinsic_definition)
Broad concept generalizing scalars in mathematics and physics
historical reasons. Vector quaternion, a quaternion with a zero real part Multivector or p-vector, an element of the exterior algebra of a vector space. Spinors
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Algebra associated to any vector space
while a more general sum of blades of arbitrary degree is called a multivector. The linear span of the k {\displaystyle k} -blades is called the k {\displaystyle
Exterior_algebra
Mathematical function, in linear algebra
{\displaystyle V} and W {\displaystyle W} be vector spaces over the same field K {\displaystyle K} , such as the real or complex numbers. A function
Linear_map
Element of a unital algebra over the field of real numbers
\\0&i\not =j.\end{cases}}} Imposing closure under multiplication generates a multivector space spanned by a basis of 2 k {\displaystyle 2^{k}} elements, { 1
Hypercomplex_number
Exterior algebraic map taking tensors from p forms to n-p forms
G b {\displaystyle a^{\mathrm {T} }Gb} , where a and b are arbitrary multivectors represented by 2 n × 1 {\displaystyle 2^{n}\times 1} column matrices
Hodge_star_operator
Representation of a tensor in Euclidean space
space, or more technically, any finite-dimensional vector space over the field of real numbers that has an inner product. Use of Cartesian tensors occurs
Cartesian_tensor
Mathematical operation on vector spaces
vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W {\displaystyle
Tensor_product
Index of articles associated with the same name
geometric product is well defined for any multivectors as arguments. A bilinear product in an algebra over a field. A Lie bracket for vectors in a Lie algebra
Vector_multiplication
Shorthand notation for tensor operations
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Einstein_notation
System of moving vectors in differential geometry
with straight lines in Euclidean space, we may say that the tangent vector field along a geodesic in a Riemannian manifold (the analogue of a straight line
Parallel_transport
Differential form of degree one or section of a cotangent bundle
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section
One-form
Type of physical quantity
of a coordinate expression of a vector field with respect to the coordinates to render it the vector field's covariant derivative. While the affine connection
Pseudotensor
Expression that may be integrated over a region
1} -forms are naturally dual to vector fields on a differentiable manifold, and the pairing between vector fields and 1 {\displaystyle 1} -forms is extended
Differential_form
Object in differential geometry
Cartan (torsion) tensor) of ∇ is the vector-valued 2-form defined on vector fields X and Y by T ( X , Y ) := ∇ X Y − ∇ Y X − [ X , Y ] {\displaystyle T(X,Y):=\nabla
Torsion_tensor
Matrix operation which flips a matrix over its diagonal
{\displaystyle n\times n} matrices over some base field k {\displaystyle k} and let L {\displaystyle L} be a field extension of k {\displaystyle k} . If A {\displaystyle
Transpose
Set of vectors used to define coordinates
structures and frames of reference. A basis B of a vector space V over a field F (such as the real numbers R {\displaystyle \mathbb {R} } or the complex
Basis_(linear_algebra)
Branch of physics which studies the behavior of materials modeled as continuous media
the presence of the body in force fields, e.g. gravitational field (gravitational forces) or electromagnetic field (electromagnetic forces), or from inertial
Continuum_mechanics
Topics referred to by the same term
syndrome, a rare liver disorder Rotor (mathematics), an even-graded multivector used to produce rotations and some other affine transformations Curl
Rotor
Mathematical operation on vectors in 3D space
product could be generalised to arbitrary multivectors in three dimensions, which results in a multivector consisting of only elements of grades 1 (1-vectors/true
Cross_product
Straight path on a curved surface or a Riemannian manifold
allows one to construct a vector field for any Ehresmann connection on the tangent bundle. For the resulting vector field to be a spray (on the deleted tangent
Geodesic
Continuous surjection satisfying a local triviality condition
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Fiber_bundle
The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is
Mathematics of general relativity
Mathematics_of_general_relativity
Tensor in differential geometry
In general relativity, the Ricci curvature tensor enters the Einstein field equations through the Einstein tensor, formed from the Ricci tensor, the
Ricci_curvature
matrix Tensor field Tensor density Lie derivative Tensor derivative Differential geometry Tensor product of fields This is an operation on fields, that does
Glossary_of_tensor_theory
Electromagnetism in general relativity
equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may deviate from the Minkowski metric)
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Array of numbers describing a metric connection
general relativity, the connection plays the role of the gravitational force field with the corresponding gravitational potential being the metric tensor.
Christoffel_symbols
Geometric structure
the spinor bundle S {\displaystyle {\mathbf {S} }\,} is called a spinor field. Let ( P , F P ) {\displaystyle ({\mathbf {P} },F_{\mathbf {P} })} be a
Spinor_bundle
Isomorphism between the tangent and cotangent bundles of a manifold
space (the space of linear functionals mapping the vector space to its base field), but not canonically. Given a fixed basis for this vector space, there
Musical_isomorphism
Array of numbers
dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly, or through their use in geometry and numerical analysis
Matrix_(mathematics)
American physicist and science educator
269–286, p. 270 A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295–12327 (1993)
David_Hestenes
Decomposition in multilinear algebra
_{m}\in F^{I_{m}}\setminus \{0\}} . The rank of a tensor depends on the field over which the tensor is decomposed. It is known that some real tensors
Tensor_rank_decomposition
Universal construction in multilinear algebra
explicitly required to define the coproduct. Let V be a vector space over a field K. For any nonnegative integer k, we define the kth tensor power of V to
Tensor_algebra
Operation that pairs a left and a right R-module into an abelian group
\mathbb {Z} _{p},\mathbb {Q} _{p}} are the ring of p-adic integers and the field of p-adic numbers. See also "profinite integer" for an example in the similar
Tensor_product_of_modules
Four-dimensional number system
{\displaystyle \operatorname {Cl} _{3,0}(\mathbb {R} ).} This is an associative multivector algebra built up from fundamental basis elements σ1, σ2, σ3 using the
Quaternion
Affine connection on the tangent bundle of a manifold
are smooth vector fields on M, i. e. smooth sections of TM. [X, Y] is the Lie bracket of X and Y. It is again a smooth vector field. The metric g can
Levi-Civita_connection
Second order tensor in vector algebra
Kronecker product Bivector Polyadic algebra Unit vector Multivector Differential form Quaternions Field (mathematics) The cross product only exists in oriented
Dyadics
Tensor index notation for tensor-based calculations
constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection
Ricci_calculus
Spinning motion in theoretical physics
well as quantum mechanics, relativistic quantum mechanics, and quantum field theory. The special Euclidean group SE(d) of direct isometries is generated
Spin_tensor
Notation used for Weyl spinors
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Van_der_Waerden_notation
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
calculus, particularly in formulations of gauge theory and topological field models. In linear algebra, the n × n {\displaystyle n\times n} identity
Kronecker_delta
Topics referred to by the same term
specifically of a differential form with a vector field Left contraction and right contraction of multivectors in a geometric algebra, extensions of the inner
Contraction
Tensor used in general relativity
pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner
Einstein_tensor
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Moment_of_inertia
Branch of mathematics
techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity
Differential_geometry
Structure defining distance on a manifold
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface)
Metric_tensor
Vector behavior under coordinate changes
(passive transformation). Thus let V be a vector space of dimension n over a field of scalars S, and let each of f = (X1, ..., Xn) and f′ = (Y1, ..., Yn) be
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Algebraic operation on coordinate vectors
abstract vector spaces over a field of scalars, being either the field of real numbers R {\displaystyle \mathbb {R} } or the field of complex numbers C {\displaystyle
Dot_product
Ways of writing certain laws of physics
any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another. However, this is not as general as
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Study of curves from a differential point of view
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Differentiable_curve
Concept in differential geometry
In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting
Exterior_covariant_derivative
Construct in differenital geometry
\tau } be any local sections of the vector bundle E, and let X be a vector field on the base space M of the bundle. Let ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle
Metric_connection
Setting of relativistic physics in geometric algebra
{L}}={\frac {1}{2}}\epsilon _{0}F^{2}-J\cdot A} The multivector-valued Euler-Lagrange equations for the field can be derived, and being loose with the mathematical
Spacetime_algebra
extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Construct allowing differentiation of tangent vector fields of manifolds
manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values
Affine_connection
Physics concept
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Covariant_transformation
Topological space that locally resembles Euclidean space
length, angles, areas (or volumes), curvature and divergence of vector fields. All differentiable manifolds (of constant dimension) can be given the structure
Manifold
thus if n ! {\displaystyle n!} is invertible, such as when working over a field of characteristic 0 {\displaystyle 0} or p > n , {\displaystyle p>n,} then
Symmetrization
Method for specifying point positions
ISBN 978-1-119-77798-4. Moon P, Spencer DE (1988). "Rectangular Coordinates (x, y, z)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and
Coordinate_system
Property of a mathematical space
proof methods are applied. The dimension of a manifold depends on the base field with respect to which Euclidean space is defined. While analysis usually
Dimension
Tensor field in Riemannian geometry
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno
Riemann_curvature_tensor
Covariant derivative of the metric tensor
Z):=(\nabla _{X}g)(Y,Z)} for X , Y , Z {\displaystyle X,Y,Z} arbitrary vector fields. In abstract index notation, this reads Q a b c = ∇ a g b c {\displaystyle
Nonmetricity_tensor
Function that is invariant under all permutations of its variables
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Symmetric_function
Abbreviation in the fields of special and general relativity
the 3d stress tensor. The electromagnetic field tensor combines the electric field and E and magnetic field B F μ ν = ( 0 − E x / c − E y / c − E z /
Four-tensor
Generalization of tensor fields
the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another (see tensor field), except that
Tensor_density
Tensor that describes the 4D geometry of spacetime
real-valued functions (since the tensor g {\displaystyle g} is a tensor field, which is defined at all points of a spacetime manifold). In order for the
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Mathematical Concept
the tensor. Nomenclature may vary according to what is traditional in the field of application. The notation is named after physicists Woldemar Voigt and
Voigt_notation
economic ambitions. At the heart of its international diplomacy is a multivector foreign policy, which aims to maintain balanced and diverse relations
Foreign relations of Kazakhstan
Foreign_relations_of_Kazakhstan
Tensor having both covariant and contravariant indices
Fiber bundle Geodesic Levi-Civita connection Linear map Manifold Matrix Multivector Pseudotensor Spinor Vector Vector space Notable tensors Mathematics Kronecker
Mixed_tensor
Provides integral formulas for all derivatives of a holomorphic function
{\displaystyle f(r)} can, in principle, be composed of any combination of multivectors. The proof of Cauchy's integral theorem for higher dimensional spaces
Cauchy's_integral_formula
Measure of the curvature of a pseudo-Riemannian manifold
for Ricci-flat manifolds and always governs the characteristics of the field equations of an Einstein manifold. In dimensions 2 and 3 the Weyl curvature
Weyl_tensor
Differential form
\omega } on M , {\displaystyle M,} one can define the divergence of a vector field X {\displaystyle X} as the unique scalar-valued function, denoted by div
Volume_form
Tensor equal to the negative of any of its transpositions
completely antisymmetric contravariant tensor field may be referred to as a k {\displaystyle k} -vector field. A tensor A that is antisymmetric on indices
Antisymmetric_tensor
Mathematical notation for tensors and spinors
Wolfgang Rindler (1984). Spinors and Space-Time, Volume 1: Two-Spinor Calculus and Relativistic Fields. Cambridge University Press. ISBN 978-0-52133707-6.
Abstract_index_notation
Antisymmetric permutation object acting on tensors
)=-\mathbf {b} \cdot (\mathbf {a\times c} )} . If F = (F1, F2, F3) is a vector field defined on some open set of R 3 {\displaystyle \mathbb {R} ^{3}} as a function
Levi-Civita_symbol
Tensor invariant under permutations of vectors it acts on
the dual of the space of homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors
Symmetric_tensor
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MULTIVECTOR FIELD
MULTIVECTOR FIELD
Surname or Lastname
English
English : topographic name for someone who lived by a field that was untilled or used for pasture, from Middle English leye ‘meadow’, ‘pasture’, ‘fallow’ + feld ‘open country’, ‘field’, or a habitational name from Leyfield in Nottinghamshire, which has the same meaning.
Surname or Lastname
Norwegian and Swedish
Norwegian and Swedish : from Old Norse hella ‘flat stone’, ‘flagstone’, ‘flat mountain’ or hellir ‘cave’. As a Nowegian name this is generally a habitational name from any of numerous farmsteads so named. As a Swedish name, it is generally ornamental.English : variant spelling of Hell 1.German : topographic name from Middle High German helle ‘hell’ (modern German Hölle), used (often in field names) in a topographic sense to denote a hollow or a wild, precipitous place.
Surname or Lastname
English
English : topographic name from Middle English infeld ‘land near the homestead or village’, or a habitational name from any of various minor places named with this term, for example In Field in Humberside or Infield House in Lancashire.
Surname or Lastname
English
English : topographic name from Middle English hauk, hauek ‘hawk’ + ley(e) ‘open country’, ‘grassland’, ‘field’, or a habitational name from Hawkesley Hall in King’s Norton, Worcestershire, named from the Old English personal name Heafoc or Old English heafoc ‘hawk’, ‘clearing’ + lēah ‘wood’, ‘clearing’.
Surname or Lastname
English
English : habitational name from a place in Nottinghamshire. The early forms, from Domesday Book to the early 13th century, show the first element uniformly as Mam-, and it is therefore likely that this was a British hill-name meaning ‘breast’ (compare Manchester), with the later addition of Old English feld ‘pasture’, ‘open country’ (see Field) as the second element. The surname is now widespread throughout Midland and southern England and is also common in Ireland.Irish : when not an importation of 1, this is an altered form of the Norman name Manville (see Mandeville).Americanized form of German and Jewish (Ashkenazic) Mansfeld, a habitational name for someone from a place so called in Saxony.
Boy/Male
Australian, British, English
A Field
Surname or Lastname
English
English : habitational name from Inkersall in Derbyshire, recorded in the 13th century as Hinkershil(l) and Hinkreshill. The final element is Old English hyll ‘hill’. The first may be the Old Norse personal name Ingvarr or an Old English byname Hynkere meaning ‘limper’. Ekwall suggests that it may represent a contracted version of Old English hīgna æcer ‘monks’ field’.The Ingersoll name in America dates back to John Ingersoll, who emigrated to the Massachusetts Bay Colony in 1629. His descendants include lawyers, public officials, and politicians in CT and PA.
Surname or Lastname
English (chiefly West Midlands and northern England)
English (chiefly West Midlands and northern England) : topographic name for someone who lived in a house (Middle English hous) in open pasture land (see Field). Reaney draws attention to the form de Felhouse (Staffordshire 1332), and suggests that this may have become Fellows.
Surname or Lastname
English (chiefly Gloucestershire and Worcestershire)
English (chiefly Gloucestershire and Worcestershire) : variant of Millward.French (northern) : from a Germanic personal name composed of the elements mil ‘good’, ‘gracious’ + hard ‘hardy’, ‘brave’, ‘strong’.Southern French : from a variant spelling of Occitan milhar ‘millet field’ (from mil ‘millet’).
Boy/Male
American, British, English
Lives in the Field
Surname or Lastname
English
English : variant of Field, from the dative plural of Old English feld ‘open country’.
Surname or Lastname
English
English : topographic name from Middle English hay, hey ‘hay’ + croft ‘field attached to a house’, ‘paddock’, or a habitational name from a minor place named with these elements, such as Haycroft in Swyncombe, Oxfordshire or Haycroft in Gloucestershire.
Surname or Lastname
English
English : habitational name from a lost minor place named with Middle English haver ‘oats’ (Old Norse hafri) + feld ‘field’.
Surname or Lastname
English
English : habitational name from Minskip in West Yorkshire, Manships Shaw in Surrey, or Manchips Field in Bishop’s Stortford, Hertfordshire, all named with the same Old English word, gemǣnscipe ‘community’, ‘fellowship’, also ‘land held in common’.
Boy/Male
English
In the field.
Surname or Lastname
German
German : nickname from the small medieval coin known as the häller or heller because it was first minted (in 1208) at the Swabian town of (Schwäbisch) Hall. Compare Hall.Jewish (Ashkenazic) : habitational name for someone from Schwäbisch Hall.German : topographic name for someone living by a field named as ‘hell’ (see Helle 3).English : topographic name for someone living on a hill, from southeastern Middle English hell + the habitational suffix -er.Dutch : from a Germanic personal name composed of the elements hild ‘strife’ + hari, heri ‘army’.Jewish (Ashkenazic) : nickname for a person with fair hair or a light complexion, from an inflected form, used before a male personal name, of German hell ‘light’, ‘bright’, Yiddish hel.
Surname or Lastname
English
English : habitational name from any of various places, such as Merryfield in Devon and Cornwall or Mirfield in West Yorkshire, all named with the Old English elements myrige ‘pleasant’ + feld ‘pasture’, ‘open country’ (see Field).
Surname or Lastname
English
English : habitational name from any of the numerous minor places so called from Old English hēah ‘high’ + feld ‘pasture’, ‘open country’ (see Field).
Surname or Lastname
English and Scottish
English and Scottish : topographic name from Middle English lees ‘fields’, ‘arable land’, plural of lee (see Lee), or from Middle English lese ‘pasture’, ‘meadow’ (Old English lǣs).English : habitational name from Leece or Lees in Lancashire, or Leese in Cheshire, all named from Old English lēas ‘woodland clearings’ (plural of lēah), or from Leece in Cumbria, which was probably named with a Celtic word, lïss ‘hall’, ‘court’, ‘the principal house in a district’.English : variant spelling of Leece 1.Scottish : reduced form of Gillies.Scottish and Irish : reduced and altered form of McLeish.Dutch : variant of Leys.
Surname or Lastname
Indian (Kashmir)
Indian (Kashmir) : Hindu (Brahman) name, probably from an ancestral personal name Madan (from Sanskrit madana ‘god of love, or infatuation’).Indian (Panjab) : Hindu (Arora) and Sikh name based on the name of an Arora clan, probably from Persian maidÄn ‘field’. The name from the Panjab is pronounced mÉ™dÄn.English : habitational name from Mathon in Herefordshire, or Mattins Farm, Radwinter, in Essex, or Martinfield Green, Saffron Walden, in Essex. The first of these is named with Old English mÄthm ‘treasure’, ‘gift’.
MULTIVECTOR FIELD
MULTIVECTOR FIELD
MULTIVECTOR FIELD
MULTIVECTOR FIELD
MULTIVECTOR FIELD
MULTIVECTOR FIELD
MULTIVECTOR FIELD
a.
Having no tent or tents, as a soldier or a field.
p. pr. & vb. n.
of Field
v. i.
To ramble here and there without any certain course or with no definite object in view; to range about; to stroll; to rove; as, to wander over the fields.
n.
The act of playing as a fielder.
a.
Having the inner part cut away, or left vacant, a narrow border being left at the sides, the tincture of the field being seen in the vacant space; -- said of a charge.
a.
Not cultivated; untitled; as, an unlabored field.
v. t.
To catch, stop, throw, etc. (the ball), as a fielder.
v. i.
To take the field.
v. i.
To stand out in the field, ready to catch, stop, or throw the ball.
n.
A work or structure of stone, brick, or other materials, raised to some height, and intended for defense or security, solid and permanent inclosing fence, as around a field, a park, a town, etc., also, one of the upright inclosing parts of a building or a room.
a.
Consisting of fields.
n.
A cannon mounted on wheels, for the use of a marching army; a piece of field artillery; -- called also field gun.
n.
The fieldfare.
a.
Engaged in the field; encamped.
n.
Any temporary fortification thrown up by an army in the field; -- commonly in the plural.
a.
Covered with growing plants or grass; green; fresh; flourishing; as, verdant fields; a verdant lawn.
n.
A ball payer who stands out in the field to catch or stop balls.
imp. & p. p.
of Field
n.
The whole surface of an escutcheon; also, so much of it is shown unconcealed by the different bearings upon it. See Illust. of Fess, where the field is represented as gules (red), while the fess is argent (silver).
a.
Open, like a field.
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