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Topics referred to by the same term
Look up subspace in Wiktionary, the free dictionary. Subspace may refer to: Subspace (mathematics), a particular subset of a parent space A subset of a
Subspace
In mathematics, vector subspace
linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when
Linear_subspace
Euclidean space without distance and angles
linear subspace (vector subspace) of a vector space produces an affine subspace of the vector space. One commonly says that this affine subspace has been
Affine_space
Filtering technique
In signal processing, signal subspace methods are empirical linear methods for dimensionality reduction and noise reduction. These approaches have attracted
Signal_subspace
1983 novel by Edward Elmer Smith
Subspace Encounter is a 1983 science fiction novel by American writer E. E. Smith, a posthumously published sequel to his Subspace Explorers. The book
Subspace_Encounter
Concept in functional analysis
functional analysis, a complemented subspace of a topological vector space X , {\displaystyle X,} is a vector subspace M {\displaystyle M} for which there
Complemented_subspace
2008 video game
more extensive single-player mode than its predecessors, known as "The Subspace Emissary". This mode is a plot-driven and side-scrolling beat 'em up featuring
Super_Smash_Bros._Brawl
Subspace preserved by a linear mapping
In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by
Invariant_subspace
Canadian series of graphic novels
becomes Scott's primary love interest. She is able to use interdimensional "Subspace" to travel long distances quickly often using Scott's head to go through
Scott_Pilgrim
Points of small height in projective space lie in a finite number of hyperplanes
In mathematics, the subspace theorem says that points of small height in projective space lie in a finite number of hyperplanes. It is a result obtained
Subspace_theorem
Inherited topology
In topology and related areas of mathematics, a subspace of a topological space ( X , τ ) {\displaystyle (X,\tau )} is a subset S of X which is equipped
Subspace_topology
9th episode of the 2nd season of Star Trek: Strange New Worlds
"Subspace Rhapsody" is the ninth episode of the second season of the American television series Star Trek: Strange New Worlds. The series follows Captain
Subspace_Rhapsody
mathematics, in linear algebra and functional analysis, a cyclic subspace is a certain special subspace of a vector space associated with a vector in the vector
Cyclic_subspace
Linear subspace generated from a vector acted on by a power series of a matrix
algebra, the order-r Krylov subspace generated by an n-by-n matrix A and a vector b of dimension n is the linear subspace spanned by the images of b under
Krylov_subspace
Lomonosov's invariant subspace theorem is a mathematical theorem from functional analysis concerning the existence of invariant subspaces of a linear operator
Lomonosov's invariant subspace theorem
Lomonosov's_invariant_subspace_theorem
1997 video game
SubSpace is a 2D space shooter video game created in 1995 and released in 1997 by Virgin Interactive which was a finalist for the Academy of Interactive
SubSpace_(video_game)
Partially unsolved problem in mathematics
In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded
Invariant_subspace_problem
Concept in linear algebra
In linear algebra, a reducing subspace W {\displaystyle W} of a linear map T : V → V {\displaystyle T:V\to V} from a Hilbert space V {\displaystyle V}
Reducing_subspace
Algebraic structure in linear algebra
if and only if all its coefficients are zero. Linear subspace A linear subspace or vector subspace W of a vector space V is a non-empty subset of V that
Vector_space
Type of mathematical space
more commonly, to a subset of a topological space that is compact in the subspace topology. Compactness was formally introduced by Maurice Fréchet in 1906
Compact_space
Vectors mapped to 0 by a linear map
mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map L : V → W between two vector
Kernel_(linear_algebra)
Various meanings of the terms
Orthogonality is a term with various meanings depending on the context. In mathematics, orthogonality is the generalization of the geometric notion of
Orthogonality
mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators
Commutator_subspace
Faster-than-light travel in science fiction
In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as
Hyperspace
Topological space that is connected
Connected and disconnected subspaces of R² In topology and related branches of mathematics, a connected space is a topological space that cannot be represented
Connected_space
Stationary Subspace Analysis (SSA) in statistics is a blind source separation algorithm which factorizes a multivariate time series into stationary and
Stationary_subspace_analysis
Numerical approximation algorithm
methods are the stationary iterative methods, and the more general Krylov subspace methods. Stationary iterative methods solve a linear system with an operator
Iterative_method
Method of data analysis
number of possible values with each dimension, complete enumeration of all subspaces becomes intractable with increasing dimensionality. This problem is known
Clustering high-dimensional data
Clustering_high-dimensional_data
Idempotent linear transformation from a vector space to itself
meaning that it maps each open set in the domain to an open set in the subspace topology of the image.[citation needed] That is, for any vector x {\displaystyle
Projection_(linear_algebra)
Concept in linear algebra
linear algebra and functional analysis, the orthogonal complement of a subspace W {\displaystyle W} of a vector space V {\displaystyle V} equipped with
Orthogonal_complement
Method in machine learning
In machine learning the random subspace method, also called attribute bagging or feature bagging, is an ensemble learning method that attempts to reduce
Random_subspace_method
Subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics
A decoherence-free subspace (DFS) is a subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they
Decoherence-free_subspaces
Mathematical concept
one of the form V ⊕ V∗. The subspace V is not unique, and a choice of subspace V is called a polarization. The subspaces that give such an isomorphism
Symplectic_vector_space
Theorem on extension of bounded linear functionals
allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem also shows that there
Hahn–Banach_theorem
Continuous, position-preserving mapping from a topological space into a subspace
mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original
Retraction_(topology)
Type of vector space in math
Hilbert space. At a deeper level, perpendicular projection onto a linear subspace plays a significant role in optimization problems and other aspects of
Hilbert_space
Quadratic form for which there is a non-zero vector on which the form evaluates to zero
space and W is a subspace of V. Then W is called an isotropic subspace of V if some vector in it is isotropic, a totally isotropic subspace if all vectors
Isotropic_quadratic_form
Subspace of n-space whose dimension is (n-1)
dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space. Two lower-dimensional
Hyperplane
Acoustic modeling approach in which all phonetic states share a common Gaussian
Subspace Gaussian mixture model (SGMM) is an acoustic modeling approach in which all phonetic states share a common Gaussian mixture model structure, and
Subspace Gaussian mixture model
Subspace_Gaussian_mixture_model
Vector space consisting of affine subsets
linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace U {\displaystyle U} is a vector space obtained by "collapsing" U {\displaystyle
Quotient space (linear algebra)
Quotient_space_(linear_algebra)
Plot device in fiction
A parallel universe, also known as an alternate universe, world, or dimension, is a plot device in fiction which uses the notion of a hypothetical universe
Parallel_universes_in_fiction
Completion of the usual space with "points at infinity"
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 n + 1. Equivalently
Projective_space
"Small" subset of a topological space
{\displaystyle A} can also be called a meagre subspace of X {\displaystyle X} , meaning a meagre space when given the subspace topology. Importantly, this is not
Meagre_set
Mathematical concept
In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output
Subspace identification method
Subspace_identification_method
In geometry, set whose intersection with every line is a single line segment
{\displaystyle \operatorname {rec} A\cap \operatorname {rec} B} is a linear subspace. If A or B is locally compact then A − B is closed. The notion of convexity
Convex_set
controlled invariant subspace of the state space representation of some system is a subspace. If the system's state is initially in the subspace, it can be controlled
Controlled_invariant_subspace
technology is becoming feasible. In the Star Trek fictional universe, subspace is a feature of space-time that facilitates faster-than-light transit,
Technology_in_Star_Trek
In linear algebra, generated subspace
elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle V} that contains S . {\displaystyle S.} It is the set
Linear_span
Mathematical set with some added structure
structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same mathematical structure
Space_(mathematics)
Fundamental space of geometry
subspaces: its Euclidean subspaces and its linear subspaces. Linear subspaces are Euclidean subspaces and a Euclidean subspace is a linear subspace if
Euclidean_space
Information sent faster than light
relay also features. In the Star Trek universe, subspace carries faster-than-light communication (subspace radio) and travel (warp drive). The Cities in
Faster-than-light communication
Faster-than-light_communication
Subset of a topological space whose closure is compact
In mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure
Relatively_compact_subspace
Approach to dimensionality reduction
Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality
Multilinear_subspace_learning
orthogonal complement of its kernel is called the initial subspace and its range is called the final subspace. Partial isometries appear in the polar decomposition
Partial_isometry
Operation in abstract algebra
of an ordered sum not as ordered pairs (v, w), but as a sum v + w. The subspace V × {0} of V ⊕ W is isomorphic to V and is often identified with V; similarly
Direct_sum_of_modules
Sum of terms, each multiplied with a scalar
vector subspaces: a vector subspace is also an affine subspace, a convex cone, and a convex set, but a convex set need not be a vector subspace, affine
Linear_combination
one-dimensional subspace on which it is positive definite (not uniquely determined), and decomposes as a direct sum of some such one-dimensional subspace, and a
Hodge_index_theorem
Vector space with a notion of nearness
vector subspace of a TVS is a vector subspace. Every finite dimensional vector subspace of a Hausdorff TVS is closed. The sum of a closed vector subspace and
Topological_vector_space
Lemma in numerical analysis of differential equations
{\displaystyle V.} Consider the same problem on a finite-dimensional subspace V h {\displaystyle V_{h}} of V , {\displaystyle V,} so, u h {\displaystyle
Céa's_lemma
Result about when a matrix can be diagonalized
Hermiticity, K n − 1 {\displaystyle {\mathcal {K}}^{n-1}} is an invariant subspace of A. To see that, consider any k ∈ K n − 1 {\displaystyle k\in {\mathcal
Spectral_theorem
In mathematics, the quotient of subspace theorem is an important property of finite-dimensional normed spaces, discovered by Vitali Milman. Let (X, ||·||)
Quotient_of_subspace_theorem
Mathematics concept
{\displaystyle V_{e}E} and H e E {\displaystyle H_{e}E} form complementary subspaces of the tangent space T e E {\displaystyle T_{e}E} . The vertical bundle
Vertical and horizontal bundles
Vertical_and_horizontal_bundles
Subset whose closure is the whole space
B {\displaystyle B} is dense in C {\displaystyle C} (in the respective subspace topology) then A {\displaystyle A} is also dense in C . {\displaystyle
Dense_set
Calculus using a logically rigorous notion of infinitesimal numbers
each of the corresponding k-dimensional subspaces Ek is T-invariant. Denote by Πk the projection to the subspace Ek. For a nonzero vector x of finite norm
Nonstandard_analysis
Term in quantum information theory
In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example
Typical_subspace
Gauge field loop operator
tangent space of the principal bundle into two subspaces known as the vertical and horizontal subspaces. The former consists of all vectors pointing along
Wilson_loop
Concept in differential geometry
Hol p ( ω ) {\displaystyle \operatorname {Hol} _{p}(\omega )} is the subspace of g spanned by elements of the form Ω q ( X , Y ) {\displaystyle \Omega
Holonomy
1965 novel by Edward Elmer Smith
Subspace Explorers is a science fiction novel by American writer E. E. "Doc" Smith. It was first published in 1965 by Canaveral Press in an edition of
Subspace_Explorers
Property of topological spaces
generated space is a space that is coherent with the family of its compact subspaces, meaning that for every set A ⊆ X , {\displaystyle A\subseteq X,} A {\displaystyle
Compactly_generated_space
Square matrix constructed from a monic polynomial
algorithms is given by Frobenius endomorphism Cayley–Hamilton theorem Krylov subspace Horn, Roger A.; Charles R. Johnson (1985). Matrix Analysis. Cambridge,
Companion_matrix
Topology determined by family of subspaces
family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. It is
Coherent_topology
Vector space with generalized dot product
{\displaystyle {\overline {H}}.} This means that H {\displaystyle H} is a linear subspace of H ¯ , {\displaystyle {\overline {H}},} the inner product of H {\displaystyle
Inner_product_space
Iterative method for approximating eigenvectors
non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices
Arnoldi_iteration
Sequence of spaces in linear algebra
an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration):
Flag_(linear_algebra)
Affine subspace of a Euclidean space
In geometry, a flat is an affine subspace, i.e. a subset of an affine space that is itself an affine space. Particularly, in the case the parent space
Flat_(geometry)
Orthonormalization of a set of vectors
\mathbf {u} _{k}\}} that spans the same k {\displaystyle k} -dimensional subspace of R n {\displaystyle \mathbb {R} ^{n}} as S {\displaystyle S} . The method
Gram–Schmidt_process
Mathematical space
parameterizes the set of all k {\displaystyle k} -dimensional linear subspaces of an n {\displaystyle n} -dimensional vector space V {\displaystyle V}
Grassmannian
Algebraic structure designed for geometry
these and several derived operations allow a correspondence of elements, subspaces and operations of the algebra with geometric interpretations. For several
Geometric_algebra
Homology for a pair of topological spaces
mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative
Relative_homology
Concept in geometry
) For each subspace the corresponding d is called its dimension. The intersection of two subspaces is always a subspace. For each subspace A of dimension
Polar_space
space c 0 {\displaystyle c_{0}} (of sequences converging to zero) as a subspace, there exists a projection from the ambient space onto c 0 {\displaystyle
Sobczyk's_theorem
Linear operator defined on a dense linear subspace
operator"); the domain of the operator is a linear subspace, not necessarily the whole space; this linear subspace is not necessarily closed; often (but not always)
Unbounded_operator
Dual pair of vector spaces
{\displaystyle B} is a vector subspace of X {\displaystyle X} then so too is B ∘ {\displaystyle B^{\circ }} a vector subspace of Y . {\displaystyle Y.} If
Dual_system
Food engineer and science-fiction author (1890–1965)
Galaxy Primes (working title: "The Girl With The Green Hair"), Subspace Explorers, and Subspace Encounter, E. E. Smith explores themes of telepathy and other
E._E._Smith
Space in mathematics and theoretical physics
collinear. The intersections of any Euclidean linear subspace with its orthogonal complement is the {0} subspace. But the definition from the previous subsection
Pseudo-Euclidean_space
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
dimensional Euclidean space into invariant subspaces of A. Every Jordan block Ji corresponds to an invariant subspace Xi. Symbolically, we put C n = ⨁ i = 1
Jordan_normal_form
Point that belongs to the closure of some given subset of a topological space
{\displaystyle X} is a topological subspace of Y {\displaystyle Y} (that is, X {\displaystyle X} is endowed with the subspace topology induced on it by Y {\displaystyle
Adherent_point
Algorithm used for frequency estimation and radio direction finding
\sigma ^{2}} and span the noise subspace U N {\displaystyle {\mathcal {U}}_{N}} , which is orthogonal to the signal subspace, U S ⊥ U N {\displaystyle {\mathcal
MUSIC_(algorithm)
Describes the fundamental group in terms of a cover by two open path-connected subspaces
{\displaystyle X} in terms of the fundamental groups of two open, path-connected subspaces that cover X {\displaystyle X} . It can therefore be used for computations
Seifert–Van_Kampen_theorem
Algebraic element satisfying some of the criteria of an inverse
{C}}(A)} and a complement subspace, and construct G {\displaystyle G} as follows. For y {\displaystyle y} 's in the former subspace, let G {\displaystyle
Generalized_inverse
German electronic music project
50 Singles chart "Gunman" (2000) – #13 DAC 2000 Top 100 Singles chart "Subspace" (2001) "Date of Expiration" (2002) "Red Queen" (2003) – #6 DAC Singles
Funker_Vogt
Process in quantum computing
and apply a unitary encoding circuit to rotate the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects
Quantum_error_correction
KC space: every compact subset is closed. k-Hausdorff: every compact subspace is Hausdorff. Hausdorff (T2): distinct points have disjoint neighborhoods
Weak_Hausdorff_space
Series of crossover fighting games
based on various game series. Brawl's was far more expansive; titled "Subspace Emissary", it was a story-based mode with several platforming levels, boss
Super_Smash_Bros.
Mathematical theory
Pontryagin. It applies to the homology theory properties of the complement of a subspace X in Euclidean space, a sphere, or another manifold. It is generalized
Alexander_duality
Method for solving continuous operator problems (such as differential equations)
method, the boundary element method for solving integral equations, Krylov subspace methods. Let us introduce Galerkin's method with an abstract problem posed
Galerkin_method
reduction subspace, or simply a central subspace, and it is denoted by S y ∣ x {\displaystyle {\mathcal {S}}_{y\mid x}} . In other words, a central subspace for
Sufficient dimension reduction
Sufficient_dimension_reduction
Notion in topology
totally ordered Y, where this order is inherited from X, is coarser than the subspace topology of the order topology of X. "Natural topology" does quite often
Natural_topology
In mathematics, vector space of linear forms
algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called
Dual_space
Comics characters
City before she moved to Toronto. She is capable of traveling through subspace and has seven evil exes who challenge Scott for her affection. She changes
List of Scott Pilgrim characters
List_of_Scott_Pilgrim_characters
SUBSPACE
SUBSPACE
SUBSPACE
SUBSPACE
Girl/Female
Muslim/Islamic
A narrator of Hadith
Boy/Male
Welsh Celtic
Son of Howell.
Boy/Male
Hindu, Indian
Messenger of God
Girl/Female
Hindu, Indian
Blessed with Lord Ganesha
Boy/Male
Arabic, Muslim, Pashtun
Elevated; Honoured
Girl/Female
Assamese, Indian
Birthless; Shiva; Vishnu; Jina
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from Venoix in Calvados, France. Spelled thus, the surname is now found principally in northeastern England.
Girl/Female
Tamil
Traveler
Boy/Male
Muslim
Fourth prayer of the day, One who has wisdom
Boy/Male
Tamil
Pundit
SUBSPACE
SUBSPACE
SUBSPACE
SUBSPACE
SUBSPACE