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Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector_bundle
In mathematics, a double vector bundle is the combination of two compatible vector bundle structures, which contains in particular the tangent T E {\displaystyle
Double_vector_bundle
Mathematical concept in particularly differential topology
secondary vector bundle structure refers to the natural vector bundle structure (TE, p∗, TM) on the total space TE of the tangent bundle of a smooth vector bundle
Secondary vector bundle structure
Secondary_vector_bundle_structure
Vector bundle of rank 1
tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a line bundle is defined as a vector bundle of
Line_bundle
the double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM
Double_tangent_bundle
Concept in algebraic geometry
The pullback of a vector bundle is a vector bundle of the same rank. In particular, the pullback of a line bundle is a line bundle. (Briefly, the fiber
Ample_line_bundle
Fiber bundle whose fibers are projective spaces
projective bundle is of the form P ( E ) {\displaystyle \mathbb {P} (E)} for some vector bundle (locally free sheaf) E. Every vector bundle over a variety
Projective_bundle
Geometric structure
g ) , {\displaystyle (M,g),\,} one defines the spinor bundle to be the complex vector bundle π S : S → M {\displaystyle \pi _{\mathbf {S} }\colon {\mathbf
Spinor_bundle
Algebraic structure in linear algebra
algebra. A vector bundle is a family of vector spaces parametrized continuously by a topological space X. More precisely, a vector bundle over X is a
Vector_space
Fiber bundle whose fibers are group torsors
principal bundle is the frame bundle F ( E ) {\displaystyle F(E)} of a vector bundle E {\displaystyle E} , which consists of all ordered bases of the vector space
Principal_bundle
Concept in algebraic geometry
canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle
Canonical_bundle
Assignment of a tensor continuously varying across a region of space
sections of the cotangent bundle, but also linear mappings of vector fields into functions. By the double-dual construction, vector fields can similarly be
Tensor_field
Special type of principal bundle
} Unlike the associated vector bundle, a complex plane bundle, the adjoint vector bundle is a orientable real vector bundle of third rank. Also since
Principal_SU(2)-bundle
Special type of principal bundle
{\displaystyle \operatorname {U} (1)} -bundle E ↠ B {\displaystyle E\twoheadrightarrow B} , there is an associated vector bundle E × U ( 1 ) C ↠ B {\displaystyle
Principal_U(1)-bundle
Straight path on a curved surface or a Riemannian manifold
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 bundle TM \ {0})
Geodesic
Possibility of a consistent definition of "clockwise" in a mathematical space
also be expressed in terms of the tangent bundle. The tangent bundle is a vector bundle, so it is a fiber bundle with structure group GL ( n , R ) {\displaystyle
Orientability
Algebraic object with geometric applications
projective modules is treated. The global sections of sections of a vector bundle over a compact space form a projective module over the ring of smooth
Tensor
Algebraic operation on coordinate vectors
numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their
Dot_product
Branch of geometry
produces a transport of unit-length tangent vectors, and thus a vector flow field on the unit tangent bundle U T ( M ) {\displaystyle UT(M)} . This is the
Contact_geometry
Non-tensorial representation of the spin group
symplectic manifold) has a Spinc structure. Likewise, every complex vector bundle on a manifold carries a Spinc structure. A number of Clebsch–Gordan
Spinor
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
In differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space)
Hopf_fibration
Specification of a derivative along a tangent vector of a manifold
covariant differentiation in a vector bundle by means of what is known today as a Koszul connection or a connection on a vector bundle. Using ideas from Lie algebra
Covariant_derivative
Mathematics concept
mathematics, the complex conjugate of a complex vector space V {\displaystyle V\,} is a complex vector space V ¯ {\displaystyle {\overline {V}}} that has
Complex conjugate of a vector space
Complex_conjugate_of_a_vector_space
Concept in differential geometry
tangent bundle TM.) The bundle of spinors πS: S → M over M is then the complex vector bundle associated with the corresponding principal bundle πP: P →
Spin_structure
Exterior algebraic map taking tensors from p forms to n-p forms
linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the
Hodge_star_operator
Bundle of linear subspaces of the tangent bundle
geometry, a contact bundle is a particular type of fiber bundle constructed from a smooth manifold. Like how the tangent bundle is the manifold that
Contact_bundle
Structure group sub-bundle on a tangent frame bundle
{\displaystyle GL(n)} -bundle, the frame bundle. In particular, every smooth manifold has a canonical vector bundle, the tangent bundle. For a Lie group G
G-structure_on_a_manifold
Second order tensor in vector algebra
that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar
Dyadics
Euclidean space without distance and angles
particular, every line bundle is trivial. More generally, the Quillen–Suslin theorem implies that every algebraic vector bundle over an affine space is
Affine_space
Differentiable function whose derivative is everywhere injective
normal bundle ν of the immersion i, which has dimension n − m, for there to be a codimension k immersion of M, there must be a vector bundle of dimension
Immersion_(mathematics)
Intrinsic geometric structures in mathematics
frame bundle. In the case of an embedded surface, this lift is very simply described in terms of orthogonal projection. Indeed, the vector bundles associated
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Vector field on tangent bundle
manifold and (TM,πTM,M) its tangent bundle. Then a vector field H on TM (that is, a section of the double tangent bundle TTM) is a semi-spray on M, if any
Spray_(mathematics)
Branch of mathematics
considerable interest in physics. The apparatus of vector bundles, principal bundles, and connections on bundles plays an extraordinarily important role in modern
Differential_geometry
Structure defining distance on a manifold
Sg defines a section of the bundle Hom(TM, T*M) of vector bundle isomorphisms of the tangent bundle to the cotangent bundle. This section has the same
Metric_tensor
Generalization of Riemannian manifolds
→ [0, +∞) defined on the tangent bundle so that for each point x of M, F(v + w) ≤ F(v) + F(w) for every two vectors v,w tangent to M at x (subadditivity)
Finsler_manifold
Kind of complex manifold
be obtained as follows: take a lattice Λ in a vector space V isomorphic to Cn considered as real vector space; then the quotient group V / Λ {\displaystyle
Complex_torus
dimension of the submanifold. Connected sum Connection Cotangent bundle – the vector bundle of cotangent spaces on a manifold. Cotangent space Covering Cusp
Glossary of differential geometry and topology
Glossary_of_differential_geometry_and_topology
Matrix operation which flips a matrix over its diagonal
tB(y, x). Here, Ψ is the natural homomorphism X → X## into the double dual. If the vector spaces X and Y have respectively nondegenerate bilinear forms
Transpose
Topological space that locally resembles Euclidean space
what a tangent vector might be, and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle. The n-sphere
Manifold
Study of curves from a differential point of view
With each turn of the spiral, both the first and second derivative vectors double in length. The second graph shows the same spiral with its arc-length
Differentiable_curve
Representation theory of an important group in physics
representation of the double cover of the group.) In a classical field theory, the physical states are sections of a Poincaré-equivariant vector bundle over Minkowski
Representation theory of the Poincaré group
Representation_theory_of_the_Poincaré_group
Subspace defined by a polynomial of degree 2 over a field
rank-m vector bundle are equal to 2 e j {\displaystyle 2e_{j}} . Here e j {\displaystyle e_{j}} is understood to mean 0 for j > m. The spinor bundles play
Quadric_(algebraic_geometry)
Array of numbers
row are called row matrices or row vectors, and those with a single column are called column matrices or column vectors. A matrix with the same number of
Matrix_(mathematics)
Relation between genus, degree, and dimension of function spaces over surfaces
(trans.). New York: Cambridge University Press. ISBN 0-521-80906-1. Vector bundles on Compact Riemann Surfaces, M. S. Narasimhan, pp. 5–6. Riemann, Bernhard
Riemann–Roch_theorem
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
can be viewed as generated by a solenoid's vector potential acting on the electron or the electron's vector potential acting on the solenoid or the electron
Aharonov–Bohm_effect
Group that is also a differentiable manifold with group operations that are smooth
acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket
Lie_group
Algebraic topology theory
{Bun} _{G}(X)} . Let E be an equivariant vector bundle on a G-manifold M. It gives rise to a vector bundle E ~ {\displaystyle {\widetilde {E}}} on the
Equivariant_cohomology
Mathematical space
this. The properties of vector bundles are thus related to the properties of the corresponding maps. In particular vector bundles inducing homotopic maps
Grassmannian
Mathematics of smooth surfaces
frame bundle so that its tangent vectors lie in a special subspace of codimension one in the three-dimensional tangent space of the frame bundle. The projection
Differential geometry of surfaces
Differential_geometry_of_surfaces
Double cover Lie group of the special orthogonal group
the spin group is the structure group of a spinor bundle. The affine connection on a spinor bundle is the spin connection; the spin connection can simplify
Spin_group
Concept in algebraic geometry
Pezzo surface is a complete non-singular surface with ample anticanonical bundle. There are some variations of this definition that are sometimes used. Sometimes
Del_Pezzo_surface
Mathematical object
admits nonvanishing vector fields (sections of its tangent bundle). One can even find three linearly independent and nonvanishing vector fields. These may
3-sphere
Economic equilibrium concept
price function P {\displaystyle P} . It takes as argument a vector representing a bundle of commodities, and returns a positive real number that represents
Competitive_equilibrium
Conserved physical quantity; rotational analogue of linear momentum
the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.
Angular_momentum
Natural moving frame in differential geometry of surfaces
curvatures. At each point p of an oriented surface, one may attach a unit normal vector u(p) in a unique way, as soon as an orientation has been chosen for the
Darboux_frame
Grouping of software code
VMware ThinApp, and the NEXTSTEP/GNUstep/Mac OS X concept of application bundles. Their heritage lies in the system for automatically launching software
Application_directory
introduced by Ward (1977), that (among other things) relates holomorphic vector bundles on 3-dimensional complex projective space CP3 to solutions of the self-dual
Penrose_transform
Formulation to quantize gauge field theories in physics
Lagrangian density with respect to a unit timelike horizontal vector field on the gauge bundle. In a quantum mechanical context it is conventionally rescaled
BRST_quantization
infinite rank vector bundle; this is the symplectic spinor construction due to Bertram Kostant. A section of the symplectic spinor bundle Q {\displaystyle
Symplectic_spinor_bundle
Subject area in mathematics
says that these are equal. When Y is a point, a vector bundle is a vector space, the class of a vector space is its dimension, and the Grothendieck–Riemann–Roch
Algebraic_K-theory
Humanist sans-serif typeface
with Office" Microsoft, retrieved April 24, 2011. Dan Kegel. "winhelp, Vector NTI, molecular biologists" WineHQ.org, September 4, 2007. Retrieved April
Tahoma_(typeface)
Mathematical game
notion of double-covering used here is a generic phenomenon, described by covering maps. Covering maps are in turn a special case of fiber bundles. The classification
Tangloids
Matrix representing a Euclidean rotation
with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: R v = [ cos θ − sin θ sin θ cos
Rotation_matrix
Solitons in Euclidean spacetime
many cases by means of twistor theory, which relates them to algebraic vector bundles on algebraic surfaces, and via the ADHM construction, or hyperkähler
Instanton
Derivative used in gauge theories
special Riemannian connection) on the tangent bundle (or the frame bundle) i.e. it acts on tangent vector fields or more generally, tensors. It is usually
Gauge_covariant_derivative
Invariant of framed knots
non-zero non-tangent vector at each point of the knot. More precisely, a framing is a choice of a non-zero section in the normal bundle of the knot, i.e.
Self-linking_number
Type of wave
In physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation
Vector_soliton
Projective variety that is also an algebraic group
isomorphism between the double dual ( A ∨ ) ∨ {\displaystyle (A^{\vee })^{\vee }} and A {\displaystyle A} (defined via the Poincaré bundle). The n-torsion of
Abelian_variety
Map from tangent space to the manifold
well-defined at every point of the tangent bundle. Intuitively speaking, the exponential map takes a given tangent vector to the manifold, runs along the geodesic
Exponential map (Riemannian geometry)
Exponential_map_(Riemannian_geometry)
Block cipher
with 2 n {\displaystyle 2n} bits of key. Therefore, Triple DES uses a "key bundle" that comprises three DES keys, K 1 {\displaystyle K1} , K 2 {\displaystyle
Triple_DES
Mathematical structure in non-Riemannian differential geometry
of two compatible Lie algebroids defined on dual vector bundles. Lie bialgebroids are the vector bundle version of Lie bialgebras. A Lie algebroid consists
Lie_bialgebroid
Space in mathematics and theoretical physics
vector bundles with self-dual connections on R 4 {\displaystyle \mathbb {R} ^{4}} (instantons) correspond bijectively to holomorphic vector bundles on
Twistor_space
Normed vector space that is complete
normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is
Banach_space
Gauge theory with affine connections
in particular, gauge theory of the fifth force. Being a vector bundle, the tangent bundle T X {\displaystyle TX} of an n {\displaystyle n} -dimensional
Affine_gauge_theory
Vector graphics editor
Michel Bouillan and Pat Beirne undertook to develop a vector-based illustration program to bundle with their desktop publishing systems. That program,
CorelDRAW
Riemannian manifold with SU(n) holonomy
bundles are not trivial, so they are Calabi–Yau manifolds according to the second but not the first definition above. On the other hand, their double
Calabi–Yau_manifold
vector space and its dual. arithmetic genus The arithmetic genus of a variety is a variation of the Euler characteristic of the trivial line bundle;
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Family of flies
without immediately killing them. Medical parasitologists view mosquitoes as vectors of disease, carrying protozoan parasites or bacterial or viral pathogens
Mosquito
Small DNA molecule within a cell
Plasmid vectors are one of many approaches that could be used for this purpose. Zinc finger nucleases (ZFNs) offer a way to cause a site-specific double-strand
Plasmid
Concept in algebraic geometry
the group PGL5g–5. Example: A vector bundle W over an algebraic curve (or over a Riemann surface) is a stable vector bundle if and only if deg ( V ) rank
Geometric_invariant_theory
Algebra based on a vector space with a quadratic form
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional
Clifford_algebra
Function that is invariant under all permutations of its variables
as functions of several vectors can be symmetric, and in fact the space of symmetric k {\displaystyle k} -tensors on a vector space V {\displaystyle V}
Symmetric_function
the Hodge vector bundle and c(E*) the total Chern class of its dual vector bundle; ψi is the first Chern class of the cotangent line bundle to the i-th
ELSV_formula
Symmetry of physical laws under a charge-conjugation transformation
equations, can be interpreted as a structure on a U(1) fiber bundle, the so-called circle bundle. This provides a geometric interpretation of electromagnetism:
C-symmetry
Indian mathematician
Nets of quadrics and vector bundles on a double plane. Math. Zeit.192, 29–43 Bhosle Usha N. (1992), Generalised parabolic bundles and applications to torsion-free
Ushadevi_Bhosle
an anti-symmetric function. The symmetrization of a symmetric map is its double, while the symmetrization of an alternating map is zero; similarly, the
Symmetrization
Instantaneous rate of change (mathematics)
function of several variables, the Jacobian matrix reduces to the gradient vector. A function of a real variable f ( x ) {\displaystyle f(x)} is differentiable
Derivative
Mathematical object studied in the field of algebraic geometry
variety comes with a natural vector bundle (or locally free sheaf in other terminology) called the tautological bundle, which is important in the study
Algebraic_variety
Lie group of Lorentz transformations
transformations, for example, a future-pointing timelike vector would be inverted to a past-pointing vector Some elements have orientation reversed by improper
Lorentz_group
Relativistic quantum mechanical wave equation
)} , which is a double cover of the Lorentz group. Under a Lorentz transformation, spacetime coordinates transform under the vector representation x
Dirac_equation
Relativistic wave equation describing massless fermions
a fiber bundle above it, with the spin group as the fiber. The spin group S p i n ( p , q ) {\displaystyle \mathrm {Spin} (p,q)} is a double cover of
Weyl_equation
British-Lebanese mathematician (1929–2019)
any vector bundle is a sum of (essentially unique) indecomposable vector bundles, and then showing that the space of indecomposable vector bundles of given
Michael_Atiyah
Reproductive structure in flowering plants
colonisation of new areas. Vectors can generally be divided into two categories: external vectors and internal vectors. External vectors include living things
Flower
Hypothetical particle with one magnetic pole
can include (but are not limited to) spin-0 monopoles or spin-1 massive vector mesons. The term "magnetic monopole" only refers to the nature of the particle
Magnetic_monopole
Describes a periodicity in the homotopy groups of classical groups
much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity
Bott_periodicity_theorem
^{n}} , functions on a manifold, vector valued functions, vector fields, or, more generally, sections of a vector bundle. In an invariant differential operator
Invariant differential operator
Invariant_differential_operator
braid Gauss–Codazzi equations Gauss–Manin connection, a connection on a vector bundle over a family of algebraic varieties Gauss–Newton line – described in
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Fair item allocation procedure
preferences of an agent are given by a vector of values - a value for each object. It is assumed that the value of a bundle for an agent is the sum of the values
Round-robin_item_allocation
degrading various types of RNA molecules. expression vector A type of vector, usually a plasmid or viral vector, designed specifically for the expression of a
Glossary of cellular and molecular biology (0–L)
Glossary_of_cellular_and_molecular_biology_(0–L)
Concept in number theory
description of line bundles on a curve can be expressed adelically. More generally, for an algebraic group G {\displaystyle G} , adelic double quotients describe
Adele_ring
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
Male
English
English name derived from the vocabulary word, from Latin nobilis, NOBLE means "noble."
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : variant of Double.In some cases, probably an altered spelling of South German Dobel or Döbel, a topographic name for someone who lived in a gorge or deep valley, Middle High German southern dialect tobel.
Boy/Male
Spanish
Victor.
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Boy/Male
Hindu, Indian
Money; Russian Currency
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : nickname from Old French doubel ‘twin’ (literally ‘double’, from Late Latin duplus, classical Latin duplex, from du(o) ‘two’ + plek, a root meaning ‘fold’).
Girl/Female
Christian, Hindu, Indian, Kannada
Money
Boy/Male
English American
Doctor; teacher.
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Male
English
Roman Latin name VICTOR means "conqueror."Â
Boy/Male
Hindu
Born during the rainy season, Money
Male
Arthurian
, sir Hector de Maris; (defender).
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
Boy/Male
Tamil
Rohiniraman | ரோஹிநிரமண
The enchanted Lord
Female
Italian
Italian diminutive form of Latin Rosa, ROSETTA means "little rose."
Girl/Female
Muslim
Instruction, Courage, Daring, Guidance
Girl/Female
Gujarati, Hindu, Indian, Pakistani
Fire
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
The Plaids; Name of a Star
Male
Arthurian
, (lordly); a king of Brittany.
Girl/Female
Hindu, Indian
Resurrection
Girl/Female
Celtic American Scottish
From the plain lands.
Girl/Female
Tamil
Dhrasika | தà¯à®°à®¾à®¸à¯€à®•à®¾
Goddess Devi
Surname or Lastname
English
English : nickname from Middle English gere ‘fit of passion’ (see Geary 3).German : possibly an altered spelling of Gier.
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
DOUBLE VECTOR-BUNDLE
n.
Among compositors, a doublet (see Doublet, 2.); among pressmen, a sheet that is twice pulled, and blurred.
a.
To be the double of; to exceed by twofold; to contain or be worth twice as much as.
a.
To increase by adding an equal number, quantity, length, value, or the like; multiply by two; to double a sum of money; to double a number, or length.
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.
Double; doubled; reduplicative; repeated.
n.
One who, or that which, doubles.
a.
Pertaining to a rector or a rectory; rectoral.
n.
The act of one that doubles; a making double; reduplication; also, that which is doubled.
n.
The state of being double or doubled.
n.
A woman who wins a victory; a female victor.
imp. & p. p.
of Double
adv.
Twice; doubly.
n.
Double-quick time, step, or march.
n.
Same as Radius vector.
n.
A game between two pairs of players; as, a first prize for doubles.
n.
An African weaver bird (Textor alector).
n.
Double beer; strong beer.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
The turning factor of a quaternion.
adv.
In a double degree; doubly.