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Topics referred to by the same term
Look up projective in Wiktionary, the free dictionary. Projective may refer to Projective geometry Projective space Projective plane Projective variety
Projective
Type of geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that
Projective_geometry
Completion of the usual space with "points at infinity"
concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus
Projective_space
Geometric concept of a 2D space with "points at infinity" adjoined
the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can
Projective_plane
Direct summand of a free module (mathematics)
the property of lifting that carries over from free to projective modules: a module P is projective if and only if for every surjective module homomorphism
Projective_module
Type of personality test
In psychology, a projective test is a personality test designed to let a person respond to ambiguous stimuli, presumably revealing hidden emotions and
Projective_test
Psychological defense mechanism
Projective identification is a term introduced by Melanie Klein and then widely adopted in psychoanalytic psychotherapy. Projective identification may
Projective_identification
Algebraic variety in a projective space
In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in
Projective_variety
Construction in group theory
especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action
Projective_linear_group
Compact non-orientable two-dimensional manifold
real projective plane, denoted R P 2 {\displaystyle \mathbf {RP} ^{2}} or P 2 {\displaystyle \mathbb {P} _{2}} , is a two-dimensional projective space
Real_projective_plane
Line with a point at infinity added
In projective geometry and mathematics more generally, a projective line is, roughly speaking, the extension of a usual line by a point called a point
Projective_line
mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy
Projective_determinacy
category theory, a projective cover of an object M is in a sense the best approximation of M by a projective object P. Projective covers are the dual
Projective_cover
Type of object in category theory
In category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used
Projective_object
Map from algebra to geometric transforms
mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P
Projective_representation
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces
Homography
Branch of mathematics
form only in projective space. For these reasons, projective space plays a fundamental role in algebraic geometry. Nowadays, the projective space Pn of
Algebraic_geometry
Concept in projective geometry
duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may be defined axiomatically as an incidence structure
Duality_(projective_geometry)
Mathematical concept
complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space
Complex_projective_space
In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space
Ovoid_(projective_geometry)
quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space
Quasi-projective_variety
Mathematical object studied in the field of algebraic geometry
called a projective algebraic set if V = Z(S) for some S. An irreducible projective algebraic set is called a projective variety. Projective varieties
Algebraic_variety
Curve from a cone intersecting a plane
{\displaystyle \pi } . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian
Conic_section
Coordinate system used in projective geometry
dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three
Homogeneous_coordinates
Model of the extended complex plane plus a point at infinity
manifolds. In projective geometry, the sphere is an example of a complex projective space and can be thought of as the complex projective line P 1 ( C
Riemann_sphere
Plane tiling corresponding to a polyhedron
In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations
Projective_polyhedron
Type of topological space
standard round metric, the measure of projective space is exactly half the measure of the sphere. Real projective spaces are smooth manifolds. On Sn, in
Real_projective_space
Concept in mathematics
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates
Quaternionic_projective_space
Fiber bundle whose fibers are projective spaces
In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle
Projective_bundle
Mathematical card game
among them. The word projective comes from the game's relation to projective spaces over the finite field with two elements. Projective Set has been studied
Projective_Set_(game)
Attributing parts of the self to others
Freud, projective identification occurs when the other person introjects, or unconsciously adopts, that which is projected onto them. In projective identification
Psychological_projection
2D surface which extends indefinitely
the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can
Plane_(mathematics)
Quotient of special unitary group by its center
isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices
Projective_unitary_group
Exact sequence used to describe the structure of an object
resolutions, projective resolutions and flat resolutions, which are left resolutions consisting, respectively of free modules, projective modules or flat
Resolution_(algebra)
In algebraic geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn]
Weighted_projective_space
In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V
Projective_orthogonal_group
Conservative political initiative in the United States
Project 2025 (also known as the 2025 Presidential Transition Project) is a political initiative published in April 2023 by the Heritage Foundation with
Project_2025
Type of transport in differential geometry
having the same unparametrized geodesics. Projective connections are modeled on the geometry of projective space. In modern terms, they may be described
Projective_connection
Assignment planned to achieve a objective
Look up project in Wiktionary, the free dictionary. A project is a type of assignment, typically involving research or design, that is carefully planned
Project
Supersymmetric-theory-dealing way in supersymmetry and quantum physics
In supersymmetry, a theory of particle physics, projective superspace is one way of dealing with N = 2 {\displaystyle {\mathcal {N}}=2} supersymmetric
Projective_superspace
A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an
Projective_cone
Generalized Euclidean space in mathematics
v ] {\displaystyle [v]} are also referred to as rays or projective rays. Each such projective ray is a copy of the nonzero complex numbers, which is topologically
Projective_Hilbert_space
Geometry
the oldest part of the theory (for the projective line), namely the Schwarzian derivative, the simplest projective differential invariant. Further work
Projective differential geometry
Projective_differential_geometry
Projective line over the real numbers
In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically
Real_projective_line
Curve defined as zeros of polynomials
zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three
Algebraic_curve
Manifold or algebraic variety of dimension n in a space of dimension n+1
a projective hypersurface, called its projective completion, whose equation is obtained by homogenizing p. That is, the equation of the projective completion
Hypersurface
Set of points in a projective line or conic
mathematics, a projective range is a set of points in projective geometry considered in a unified fashion. A projective range may be a projective line or a
Projective_range
Family of geometric objects with a common property
with the above definition since in the unique projective extension of the affine plane to a projective plane a single point (point at infinity) is added
Pencil_(geometry)
In projective geometry, points that define coordinates
and more specifically in projective geometry, a projective frame or projective basis is a tuple of points in a projective space that can be used for
Projective_frame
2021 science-fiction novel by Andy Weir
Project Hail Mary is a 2021 hard science fiction novel by American writer Andy Weir. It centers on school teacher and former biologist Ryland Grace, who
Project_Hail_Mary
Circle-like pointset in a geometric plane
a projective space. A generalization of the oval concept is an abstract oval, which is a structure that is not necessarily embedded in a projective plane
Oval_(projective_plane)
a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but
Fake_projective_plane
Oriented projective geometry is an oriented version of real projective geometry. Whereas the real projective plane describes the set of all unoriented
Oriented_projective_geometry
Point found separated from another, given a point pair
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following
Projective_harmonic_conjugate
Locus of the zeros of a polynomial of degree two
affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below. In coordinates x1, x2, ..., xD+1
Quadric
Concept in geometry
dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at
Point_at_infinity
Geometric shape
Linnaeus Wayland (1917-01-01). Projective Geometry. McGraw-Hill book Company, Incorporated. G. B. Halsted (1906) Synthetic Projective Geometry, page 20 Protter
Cone
Descriptive set theory concept
is projective iff it is definable in the language of second-order arithmetic from some real parameter. A similar relationship between the projective hierarchy
Projective_hierarchy
projector. Projective texture mapping is useful in a variety of lighting techniques and it is the starting point for shadow mapping. Projective texture mapping
Projective_texture_mapping
Topics referred to by the same term
Look up projection, projecting, projective, or projector in Wiktionary, the free dictionary. Projection or projections may refer to: Projection (physics)
Projection
finite projective plane of even order. A k-arc which can not be extended to a larger arc is called a complete arc. In the Desarguesian projective planes
Arc_(projective_geometry)
Projective plane
In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions. The Cayley plane was discovered in 1933
Cayley_plane
geometry, smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle
Smooth_projective_plane
Relation between Lie algebras depicted as a square
the octonionic projective plane – FII, dimension 16 = 2 × 8, F4 symmetry, Cayley projective plane P2(O), the bioctonionic projective plane – EIII, dimension
Freudenthal_magic_square
Complex algebraic variety
In mathematics, a fake projective space is a complex algebraic variety that has the same Betti numbers as some projective space, but is not isomorphic
Fake_projective_space
Projective construction in ring theory
mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A)
Projective_line_over_a_ring
Invariant in projective geometry
is essentially the only projective invariant of a quadruple of collinear points; this underlies its importance for projective geometry. The cross-ratio
Cross-ratio
Type of algebraic variety
is projective, there exist nonsingular complete varieties in dimension 3 and higher which are not projective. The first examples of non-projective complete
Complete_variety
map induces a projectivity. The converse of this observation (except for the projective line) is the fundamental theorem of projective geometry. Thus
Semilinear_map
Theorem about orthocenter and polars in circle geometry
(also known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. It is named after French
Brokard's_theorem
Subspace of n-space whose dimension is (n-1)
the solution of a single linear equation. Projective hyperplanes are used in projective geometry. A projective subspace is a set of points with the property
Hyperplane
Nonexistence result for combinatorial block designs
a projective plane, the theorem (which in this case is referred to as the Bruck–Ryser theorem) can be stated as follows: If a finite projective plane
Bruck–Ryser–Chowla_theorem
2-dimensional complex projective space
homogeneous coordinates in the traditional sense of projective geometry. The Betti numbers of the complex projective plane are 1, 0, 1, 0, 1, 0, 0, ..... The middle
Complex_projective_plane
Geometric system with a finite number of points
Galois geometries, since any finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the
Finite_geometry
Type of mathematical curve
projective space of dimension three over the field of the complex numbers (or over an algebraic closure of k {\displaystyle k} ), whose projective
Cubic_plane_curve
Ring whose ideals are projective
a ring R is called hereditary if all submodules of projective modules over R are again projective. If this is required only for finitely generated submodules
Hereditary_ring
Ruled surface over the projective line
is the P 1 {\displaystyle \mathbb {P} ^{1}} -bundle (a projective bundle) over the projective line P 1 {\displaystyle \mathbb {P} ^{1}} , associated to
Hirzebruch_surface
Concept in projective geometry
In projective geometry, a correlation is a transformation of a d-dimensional projective space that maps subspaces of dimension k to subspaces of dimension
Correlation (projective geometry)
Correlation_(projective_geometry)
Topics referred to by the same term
Project A may refer to: Project A (film), 1983 martial arts action-comedy film Project A Part II, 1987 Hong Kong martial arts action-comedy film Project
Project_A
Number used in algebraic geometry
In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety with n hyperplanes in
Degree of an algebraic variety
Degree_of_an_algebraic_variety
Branch of finite geometry
a Galois geometry may be defined as a projective space over a finite field. Objects of study include affine and projective spaces over finite fields and various
Galois_geometry
fundamental geometric statement on projective spaces: the Euler sequence. The negativity of the canonical line bundle makes projective spaces prime examples of
Algebraic geometry of projective spaces
Algebraic_geometry_of_projective_spaces
UFO conspiracy theory
06222; -71.87389 The Montauk Project is a conspiracy theory that alleges there were a series of United States government projects conducted at Camp Hero or
Montauk_Project
Map in projective geometry
embedding is a map used in projective geometry to consider the cartesian product of two projective spaces as a projective variety. It is named after Corrado
Segre_embedding
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
equal to 1 is simple for all odd n > 1, when it is isomorphic to the projective special linear group. The first classification of simple Lie groups was
Simple_Lie_group
Shape
egg. The term is not very specific, but in some areas of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition
Oval
Technique for childhood psychology assessments
of projective tests are subjective in nature. The limitations of projective tests should be considered. It is generally a good idea to use projective tests
Kinetic_family_drawing
Projective analogue of the spectrum of a ring
schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental
Proj_construction
Theorem in the mathematical formulation of quantum mechanics
then it is a projective representation G → PGL(H) in the mathematical sense, while its representative on Hilbert space is a projective representation
Wigner's_theorem
commutative ring assigned to any projective variety. If V is an algebraic variety given as a subvariety of projective space of a given dimension N, its
Homogeneous_coordinate_ring
abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; where
Kaplansky's theorem on projective modules
Kaplansky's_theorem_on_projective_modules
Type of mathematical space
generalized flag variety is defined to mean a projective homogeneous variety, that is, a smooth projective variety X over a field F with a transitive action
Generalized_flag_variety
2026 operation to open the Strait of Hormuz
Operation Project Freedom is a United States military operation launched on 4 May 2026 to escort merchant ships, in response to Iranian attacks on shipping
Operation_Project_Freedom
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes
Hilbert_scheme
Projective plane not satisfying Desargues' theorem
in all projective spaces of dimension not 2; in other words, the only projective spaces of dimension not equal to 2 are the classical projective geometries
Non-Desarguesian_plane
Algebraic structure in ring theory
projective, or torsion-free. In particular, every flat module is torsion-free, every projective module is flat, and every free module is projective.
Flat_module
Algebraic variety containing an algebraic torus
of toric varieties are affine space, projective spaces, products of projective spaces and bundles over projective space. A precise definition is that a
Toric_variety
General concept and operation in mathematics
electric fields. In some projective planes, it is possible to find geometric transformations that map each point of the projective plane to a line, and each
Duality_(mathematics)
CIA program involving illegal experimentation on human test subjects (1953–1973)
verbal and sexual abuse, and other forms of torture. Project MKUltra was preceded by Project Artichoke. It was organized through the CIA's Office of
MKUltra
British and American filmmaker (born 1970)
this period in his career, Nolan had little to no success getting his projects off the ground, facing several rejections; he added, "[T]here's a very
Christopher_Nolan
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE
Boy/Male
Hindu
Love to Meet different persons, A friend
Boy/Male
Indian, Sanskrit
Mine of Victory
Boy/Male
Tamil
Kabalikrut | கபாலீகரத
Swallower of the Sun
Boy/Male
Muslim
Grace of the truth i.e. Allah
Male
English
English surname transferred to forename use, from the Norman French baronial name d'Airelle, DARRELL means "from Airelle."
Girl/Female
American, British, Christian, Czech, Czechoslovakian, Danish, English, Finnish, French, German, Greek, Latin, Scandinavian
Follower of Christ; Anointed; Christ Bearer
Boy/Male
Teutonic
Friend of peace.
Boy/Male
Hindu
Rough, Rugged
Girl/Female
Tamil
Aahladita | ஆஹலாதிதா
Bubbling with delight
Boy/Male
Muslim
Morning star, Always victorious, Warrior, Prosperous
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE