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Module over the algebra of quaternions
quaternionic vector space is a module over the quaternions. Since the quaternion algebra is division ring, these modules are referred to as "vector spaces"
Quaternionic_vector_space
Concept in geometry
\bigwedge ^{2k}T^{*}M=\bigwedge ^{4n-2k}T^{*}M.} If we regard the quaternionic vector space H n ≅ R 4 n {\displaystyle \mathbb {H} ^{n}\cong \mathbb {R} ^{4n}}
Quaternionic_manifold
Representation of a group or algebra in terms of an algebra with quaternionic structure
representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure, i.e., an antilinear
Quaternionic_representation
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
(pseudo-)Riemannian manifold whose geodesics are reversible
summand acting like the unit quaternions on a quaternionic vector space. Thus the quaternion-Kähler symmetric spaces are easily read off from the classification
Symmetric_space
Non-tensorial representation of the spin group
complex vector space that can be associated with Euclidean space. Spinors can be thought of as companion geometric objects to Euclidean space that, like
Spinor
Geometric model of the physical space
textbook Vector Analysis written by Edwin Bidwell Wilson based on Gibbs' lectures. Further development came in the abstract formalism of vector spaces, with
Three-dimensional_space
Type of Riemannian manifold
g,I,J,K)} is a hyperkähler manifold, then the tangent space TxM is a quaternionic vector space for each point x of M, i.e. it is isomorphic to H n {\displaystyle
Hyperkähler_manifold
Karlhede, and U. Lindström et al. (1987) to a torus acting on a quaternionic vector space. Roger Bielawski and Andrew S. Dancer (2000) gave a systematic
Hypertoric_variety
Type of group in mathematics
linear in the second. For quaternionic vector spaces one usually works with right H {\displaystyle \mathbb {H} } -vector spaces. In that setting the relevant
Classical_group
Smooth manifold with an inner product on each tangent space
real projective space which are also symmetric, as are complex hyperbolic space, quaternionic hyperbolic space, and Cayley hyperbolic space, which are instead
Riemannian_manifold
Correspondence between quaternions and 3D rotations
that specifies a rotation as to axial vectors. In quaternionic formalism the choice of an orientation of the space corresponds to order of multiplication:
Quaternions and spatial rotation
Quaternions_and_spatial_rotation
Mathematical group
symplectic group of a 2 n {\displaystyle 2n} -dimensional symplectic vector space over a field F {\displaystyle \mathbb {F} } . A related but different
Symplectic_group
Completion of the usual space with "points at infinity"
projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension
Projective_space
Mathematical concept
complex projective space is the space of complex lines through the origin of an (n+1)-dimensional complex vector space. The space is denoted variously
Complex_projective_space
Matrix representing a Euclidean rotation
otherwise specified. Vectors or forms The vector space has a dual space of linear forms, and the matrix can act on either vectors or forms. Consider the
Rotation_matrix
Describes a periodicity in the homotopy groups of classical groups
for the infinite symplectic group, Sp, the space BSp is the classifying space for stable quaternionic vector bundles, and Bott periodicity states that
Bott_periodicity_theorem
Mnemonic for 3D vectors orientations and rotations
simplifies vector formalism. Following a substantial debate, the mainstream shifted from Hamilton's quaternionic system to Gibbs's three-vectors system.
Right-hand_rule
Manifold of all orthonormal k-frames in n-dimensional Euclidean space
generally, the construction applies to any real, complex, or quaternionic inner product space. In some contexts, a non-compact Stiefel manifold is defined
Stiefel_manifold
Particular projective representations of the orthogonal or special orthogonal groups
that the triple i, j and k:=ij make S into a quaternionic vector space SH. This is called a quaternionic structure. There is an invariant complex antilinear
Spin_representation
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
^{n+1}} (quaternionic n-space) and factor out by unit quaternion (= S 3 {\displaystyle S^{3}} ) multiplication to get the quaternionic projective space H P
Hopf_fibration
Algebraic structure designed for geometry
1844; and vector analysis, developed out of quaternionic analysis in the late 19th century by Gibbs and Heaviside. The legacy of quaternionic analysis
Geometric_algebra
Complex vector of electromagnetic fields
Riemann–Silberstein vector in contemporary parlance, a transition is made: With the advent of spinor calculus that superseded the quaternionic calculus, the
Riemann–Silberstein_vector
one symmetric spaces, together with real and quaternionic hyperbolic spaces, classification to which must be added one exceptional space, the Cayley plane
Complex_hyperbolic_space
Concept in geometry
In geometry, a quaternionic polytope is a generalization of a polytope in real space to an analogous structure in a quaternionic module, where each real
Quaternionic_polytope
Function theory with quaternion variable
In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of
Quaternionic_analysis
Equations describing classical electromagnetism
and a matrix representation of Maxwell's equations. Historically, a quaternionic formulation was used. Maxwell's equations are partial differential equations
Maxwell's_equations
complex vector space. Sometimes (for example in physics), the term complex representation is reserved for a representation on a complex vector space that
Complex_representation
Moduli space of the Yang–Mills equations
I}\subset X} (or alternatively a connection since the latter space is an affine vector space, which makes the isomorphism non-canonical) and is then given
Yang–Mills_moduli_space
Concept in differential geometry
Date incompatibility (help) Kraines, Vivian Yoh (1965), "Topology of quaternionic manifolds", Bull. Amer. Math. Soc., 71, 3, 1 (3): 526–7, doi:10
Holonomy
Relates the geometric vector bundles to algebraic projective modules
smooth vector bundles on a smooth manifold (real, complex, or quaternionic). His topological variant is about continuous (real or complex) vector bundles
Serre–Swan_theorem
Type of representation in representation theory
sum of real and quaternionic representations is neither real nor quaternionic in general. A representation on a complex vector space can also be isomorphic
Real_representation
Schur indicator −1, called a quaternionic representation. Moreover, every irreducible representation on a complex vector space can be constructed from a
Frobenius–Schur_indicator
Super vector space forming base superspace for supersymmetric field theories
{N}}} . The underlying supermanifold of super Minkowski space is isomorphic to a super vector space given by the direct sum of ordinary Minkowski spacetime
Super_Minkowski_space
Mathematical object
quaternion; that is, a quaternion that satisfies τ2 = −1. This is the quaternionic analogue of Euler's formula. Now the unit imaginary quaternions all lie
3-sphere
Special type of principal bundle
is exactly the infinite quaternionic projective space H P ∞ {\displaystyle \mathbb {H} P^{\infty }} . For a topological space B {\displaystyle B} , let
Principal_SU(2)-bundle
Theorem in quantum mechanics
theorem to be applicable, the space on which measurements are defined must be a real or complex Hilbert space, or a quaternionic module. (Gleason's argument
Gleason's_theorem
Generalization of the concept of directional derivative
between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gateaux differential is often
Gateaux_derivative
Element of a unital algebra over the field of real numbers
{\displaystyle \mathbb {H} ^{\otimes 3}=M(4,\mathbb {H} )} yields a quaternionic matrix and its even subalgebra H ⊗ 2 ⊗ R C {\displaystyle \mathbb {H}
Hypercomplex_number
Mathematical theorem
infinite-dimensional vector spaces. It states that any orthomodular form that has an infinite orthonormal set is a Hilbert space over the real numbers
Solèr's_theorem
Fiber bundle whose fibers are group torsors
is a principal S p ( 1 ) {\displaystyle Sp(1)} -bundle over quaternionic projective space H P n {\displaystyle \mathbb {H} \mathbb {P} ^{n}} . We then
Principal_bundle
Hypercomplex number system
e_{3}} , ..., e 15 {\displaystyle e_{15}} , which form a basis of the vector space of sedenions. Every sedenion can be represented in the form x = x 0 e
Sedenion
Geometric concept of a 2D space with "points at infinity" adjoined
plane can also be constructed by starting from R3 viewed as a vector space, see § Vector space construction below. The points of the Moulton plane are the
Projective_plane
Vector bundle of rank 1
defined as a vector bundle of rank 1. Line bundles are specified by choosing a one-dimensional vector space for each point of the space in a continuous
Line_bundle
Space of vacuum states
branch must be a quaternionic Kähler manifold. In extended supergravities with N>2 the moduli space must always be a symmetric space. Riemann, Bernhard
Moduli_(physics)
representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ω) which preserves the symplectic form ω. Here ω is a nondegenerate
Symplectic_representation
Mathematical concept
operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors a, b in R 7 {\displaystyle \mathbb {R} ^{7}} a vector a × b also
Seven-dimensional cross product
Seven-dimensional_cross_product
In 3 and 4 dimensions Clifford analysis is sometimes referred to as quaternionic analysis. When n = 4, the Dirac operator is sometimes referred to as
Clifford_analysis
geometry used to describe the physical phenomena of quantum physics Quaternionic analysis Ramsey theory the study of the conditions in which order must
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Classification in abstract algebra
algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the finite-dimensional Clifford algebras for a nondegenerate quadratic
Classification of Clifford algebras
Classification_of_Clifford_algebras
Manifold
variety Quaternionic manifold Real-complex manifold One must use the open unit ball in the C n {\displaystyle \mathbb {C} ^{n}} as the model space instead
Complex_manifold
Double cover Lie group of the special orthogonal group
form applied to a vector v ∈ V {\displaystyle v\in V} . The resulting space is finite dimensional, naturally graded (as a vector space), and can therefore
Spin_group
a Hopf manifold (Hopf 1948) is obtained as a quotient of the complex vector space (with zero deleted) ( C n ∖ 0 ) {\displaystyle ({\mathbb {C} }^{n}\backslash
Hopf_manifold
repeated. KSp0(X) is the ring of stable equivalence classes of quaternionic vector bundles over X. Bott periodicity implies that the K-groups have period
List_of_cohomology_theories
function whose domain is the entire complex plane. Quaternionic function: a function whose domain is quaternionic. Hypercomplex function: a function whose domain
List_of_types_of_functions
American scientist (1839–1903)
to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely
Josiah_Willard_Gibbs
Fundamental construction of differential calculus
etc. The Fréchet derivative defines the derivative for general normed vector spaces V , W {\displaystyle V,W} . Briefly, a function f : U → W {\displaystyle
Generalizations of the derivative
Generalizations_of_the_derivative
Mathematical operation
homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform is a mapping between linear
Cayley_transform
Study of complex manifolds and several complex variables
complex structures I , J , K {\displaystyle I,J,K} which satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − Id {\displaystyle
Complex_geometry
Supergravity in eleven dimensions
7-sphere, which can be acquired by embedding the 7-sphere in a quaternionic projective space, with this giving a gauge group of SO ( 5 ) × SU ( 2 ) {\displaystyle
Eleven-dimensional supergravity
Eleven-dimensional_supergravity
Four finite groups derived from the Leech lattice
Hall–Janko group J2 (order 604,800) as the quotient of the group of quaternionic automorphisms of Λ by the group ±1 of scalars. The seven simple groups
Conway_group
Polish-American physicist (1872–1948)
22 579–86 & 24:783–4 1912: Quaternionic form of relativity, Phil. Mag. 14 1912 790–809 1913: Second memoir on quaternionic relativity, Phil. Mag. 15 1913
Ludwik_Silberstein
Quaternion of norm 1 (unit quaternion)
binary icosahedral group. A hyperbolic versor is a generalization of quaternionic versors to indefinite orthogonal groups, such as Lorentz group. It is
Versor
Concept in mathematics
character is real, complex, or quaternionic. They are examples of Schur functors. They are defined as follows. Let V be a vector space. Define an endomorphism
Tensor product of representations
Tensor_product_of_representations
Structure group sub-bundle on a tangent frame bundle
even-dimensional real vector space is isomorphic to the underlying real space of a complex vector space: it admits a linear complex structure. A real vector bundle admits
G-structure_on_a_manifold
On products on sums of squares
)+s\ \mathbf {v} +t\ \mathbf {w} +\mathbf {v} \times \mathbf {w} .} The quaternionic conjugate of q is defined by q ¯ = t − v , {\displaystyle {\overline
Lagrange's_identity
Smooth manifold
half-dimensional space is the annihilator of a nowhere vanishing pure spinor then M is a generalized Calabi–Yau manifold. Almost quaternionic manifold – Concept
Almost_complex_manifold
Mathematical result in differential geometry
kernel and cokernel of the Dirac operator have a quaternionic structure, so as complex vector spaces they have even dimensions, so the index is even.
Atiyah–Singer_index_theorem
Regular object in four dimensional geometry
represent the 32 root vectors of the B4 and C4 simple Lie groups. The 48 vertices (or strictly speaking their radius vectors) of the union of the 24-cell
24-cell
Representations of finite groups, particularly on vector spaces
structures. Here the focus is in particular on operations of groups on vector spaces. Nevertheless, groups acting on other groups or on sets are also considered
Representation theory of finite groups
Representation_theory_of_finite_groups
Hypercomplex number system
basis with signature (− − − −) and is given in terms of the following 7 quaternionic triples (omitting the scalar identity element): ( I , j , k ) , ( i
Octonion
Generalized sphere of dimension n (mathematics)
-sphere, Lie group structure Sp(1) = SU(2). 4-sphere Homeomorphic to the quaternionic projective line, H P 1 {\displaystyle \mathbf {HP} ^{1}} . SO
N-sphere
Spin representations of the SO(3) group
Spinors can be constructed directly from isotropic vectors in 3-space without using the quaternionic construction. To motivate this introduction of spinors
Spinors_in_three_dimensions
Method of constructing instanton solutions
Instantons." The ADHM construction uses the following data: complex vector spaces V and W of dimension k and N, k × k complex matrices B1, B2, a k × N
ADHM_construction
Group of unitary matrices
is working with a vector space over the complex numbers. Given a Hermitian form Ψ {\displaystyle \Psi } on a complex vector space V {\displaystyle V}
Unitary_group
Type of Riemannian manifold with constant Jacobi operator spectrum
{\displaystyle \mathbb {CH} ^{n}} , quaternionic projective spaces H P n {\displaystyle \mathbb {HP} ^{n}} , quaternionic hyperbolic spaces H H n {\displaystyle \mathbb
Osserman_manifold
Special tangential structure
In spin geometry, a spinh structure (or quaternionic spin structure) is a generalization of a spin structure. In mathematics, these are used to describe
Spinh_structure
v+W\mapsto gv+W} . quaternionic A quaternionic representation of a group G is a complex representation equipped with a G-invariant quaternionic structure. quiver
Glossary of representation theory
Glossary_of_representation_theory
Quaternions with complex number coefficients
Complex Quaternions and Maxwell's Equations. Furey 2012. L. Silberstein, Quaternionic Form of Relativity, Philos. Mag. S., 6, Vol. 23, No. 137, pp. 790-809
Biquaternion
conventional projective space to a point. More concretely, in a real projective space, complex projective space or quaternionic projective space K P n {\displaystyle
Stunted_projective_space
Mathematics term
that if G acts unitarily on a Hilbert space and has "almost invariant vectors", then it has a nonzero invariant vector. The formal definition, introduced
Kazhdan's_property_(T)
Low-rank isomorphisms in mathematics
Minkowski space with a unitary group of signature ( 2 , 2 ) {\displaystyle (2,2)} . Twistor space is naturally a complex 4-dimensional vector space equipped
Exceptional isomorphisms of classical groups
Exceptional_isomorphisms_of_classical_groups
Natural number
e_{i}\pm e_{j}:1\leq i<j\leq 4\}} in four-dimensional Euclidean space. In quaternionic form, the same configuration may be identified with the 24 unit
24_(number)
Theory of supergravity in four dimensions
graviton and a gravitino, but can also have an arbitrary number of chiral and vector supermultiplets, with supersymmetry imposing stringent constraints on how
4D_N_=_1_supergravity
American mathematician
Zbl 0553.32008. Galicki, K.; Lawson, H. Blaine Jr. (1988). "Quaternionic reduction and quaternionic orbifolds". Mathematische Annalen. 282 (1): 1–21. doi:10
H._Blaine_Lawson
characteristic 2 {\displaystyle 2} . Let W {\displaystyle W} be a symplectic vector space over F {\displaystyle F} , and S p ( W ) {\displaystyle Sp(W)} the symplectic
Theta_correspondence
Four-dimensional associative algebra over the reals
ki = j = −ik, and also ijk = 1. So, the split-quaternions form a real vector space of dimension four with {1, i, j, k} as a basis. They form also a noncommutative
Split-quaternion
Special mathematical functions defined on the surface of a sphere
3-sphere. The spaces of spherical harmonics on the 3-sphere are certain spin representations of SO(3), with respect to the action by quaternionic multiplication
Spherical_harmonics
288-cell is the only non-regular 4-polytope which is the convex hull of a quaternionic group, disregarding the infinitely many dicyclic (same as binary dihedral)
Truncated_24-cells
Riemannian metric on the space of mixed states of a quantum system
of quantum and classical Fisher information to two-level complex and quaternionic and three-level complex systems". Journal of Mathematical Physics. 37
Bures_metric
Metric on a complex projective space endowed with Hermitian form
and 1905 by Guido Fubini and Eduard Study. A Hermitian form in (the vector space) Cn+1 defines a unitary subgroup U(n+1) in GL(n+1,C). A Fubini–Study
Fubini–Study_metric
Irish physicist (1875–1950)
A:1–9 BHL link via Biodiversity Heritage Library A.W. Conway (1912) "The quaternionic form of relativity", Philosophical Magazine (6) 24:208 George Temple
Arthur_W._Conway
Four-dimensional analog of the dodecahedron
4-coordinate point (w,x,y,z) is a vector in 4D space from (0,0,0,0). Four-dimensional real space is a vector space: any two vectors can be added or multiplied
120-cell
Type of group representation for locally compact groups
functors. Blattner's conjecture Holomorphic discrete series representation Quaternionic discrete series representation Atiyah, Michael; Schmid, Wilfried (1977)
Discrete series representation
Discrete_series_representation
matrix which, when multiplied with a vector, has the same effect as subtracting the mean of the components of the vector from every component. Correlation
List_of_named_matrices
Every polynomial has a real or complex root
Eilenberg–Niven theorem, a generalization of the theorem to polynomials with quaternionic coefficients and variables Hilbert's Nullstellensatz, a generalization
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Generalization of a polytope in real space
a real 2n-dimensional vector space. A complex n-polytope in complex n-space is the analogue of a real n-polytope in real n-space. However, there is no
Complex_polytope
Matrix-valued random variable
{1}{Z_{{\text{GSE}}(n)}}}e^{-n\mathrm {tr} H^{2}}} on the space of n × n Hermitian quaternionic matrices, e.g. symmetric square matrices composed of quaternions
Random_matrix
French mathematician
(1995), "On some structure equations for almost quaternionic Hermitian manifolds", Complex Structures and Vector Fields: 114–135. Dominic Joyce, Compact manifolds
Edmond_Bonan
Classification system for symmetry groups in geometry
"Quaternionic modular groups". Linear Algebra and Its Applications. 295 (1–3): 159–189. doi:10.1016/S0024-3795(99)00107-X. The Crystallographic Space groups
Coxeter_notation
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
Biblical
a guard of four soldiers,...and delivered him to four quaternions of soldiers to guard him...
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
Latin American Spanish
Conqueror.
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Arthurian
, sir Hector de Maris; (defender).
Boy/Male
English American
Doctor; teacher.
Boy/Male
Spanish
Victor.
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
Spanish American Shakespearean Greek Latin
Tenacious.
Boy/Male
Christian & English(British/American/Australian)
Steadfast
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
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
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
Christian & English(British/American/Australian)
Conqueror
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Italian, Latin, Portuguese, Shakespearean, Spanish
Steadfast; Anchor; Holds Fast; Star; Coined from Esther Vanhomrigh; Tenacious; Defend; Hold Fast; Coined from Esther Vanho
Male
English
Roman Latin name VICTOR means "conqueror."Â
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
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."
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
Surname or Lastname
English
English : from Middle English pertriche ‘partridge’ (via Old French and Latin from Greek perdix), either a metonymic occupational name for a hunter of the bird or a nickname for someone with some fancied resemblance to it, or a habitational name for someone living at a house distinguished by the sign of a partridge. This surname has been established in Ireland since the 17th century. As an American family name, it has probably absorbed some cases of other European surnames with the same meaning, e.g. Italian Pernice.
Boy/Male
Hindu
The Sun God, Another name for Surya
Girl/Female
Arabic, Muslim
Cheerful; Be Glad
Boy/Male
Hindu, Indian
Good
Boy/Male
Egyptian
God of the moon.
Girl/Female
Norse
Warrior woman.
Boy/Male
French
Divine peace.
Biblical
a ruling; commanding; coming down
Boy/Male
Hindu, Indian
Beautiful
Girl/Female
Indian
All
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
QUATERNIONIC VECTOR-SPACE
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
The turning factor of a quaternion.
n.
A woman who wins a victory; a female victor.
n.
The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
a.
Of or pertaining to victory, or a victor' being a victor; bringing or causing a victory; conquering; winning; triumphant; as, a victorious general; victorious troops; a victorious day.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
a.
Pertaining to a rector or a rectory; rectoral.
n.
Same as Radius vector.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
n.
The chief elective officer of some universities, as in France and Scotland; sometimes, the head of a college; as, the Rector of Exeter College, or of Lincoln College, at Oxford.
v. t.
To confer a doctorate upon; to make a doctor.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
n.
An astronomical instrument, the limb of which embraces a small portion only of a circle, used for measuring differences of declination too great for the compass of a micrometer. When it is used for measuring zenith distances of stars, it is called a zenith sector.
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
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.
v. t.
To divide into quaternions, files, or companies.
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.
n.
A contrivance for removing superfluous ink or coloring matter from a roller. See Doctor, 4.
n.
An African weaver bird (Textor alector).