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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
Term in quantum information theory
the received state in the average typical subspace?" He can do this operationally by performing a typical subspace measurement corresponding to { Π ρ
Classical_capacity
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
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
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
Mathematical concept
= Tp(M) ⊕ (Tp(M))∗. The complex analog to a Lagrangian subspace is a real subspace, a subspace whose complexification is the whole space: W = V ⊕ J V
Symplectic_vector_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
2008 video game
more extensive single-player mode than its predecessors, known as "The Subspace Emissary". This mode is a side-scrolling and plot-driven beat 'em up featuring
Super_Smash_Bros._Brawl
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
Hungarian mathematical physicist and quantum information theorist (1953–2018)
Known for Quantum Stein's lemma Petz recovery map monotone metric typical subspace theorem variational formula for the quantum relative entropy Awards
Dénes_Petz
Maximum rate of a quantum channel
subadditivity of quantum entropy. Classical capacity Quantum capacity Typical subspace Christoph Adami and Nicolas J. Cerf. von Neumann capacity of noisy
Entanglement-assisted classical capacity
Entanglement-assisted_classical_capacity
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
utilizes the von Neumann entropy and its variants and the notion of typical subspace to present the capacities of quantum communication channels. The second
Mark_Wilde
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)
Information held in the state of a quantum system
Quantum information science Quantum statistical mechanics Qubit Qutrit Typical subspace Vedral, Vlatko (2006). Introduction to Quantum Information Science
Quantum_information
Algorithm to approximate functions
referred to as Remes algorithm or Reme algorithm. A typical example of a Chebyshev space is the subspace of Chebyshev polynomials of order n in the space
Remez_algorithm
Robot used in manufacturing
robot and the 3 orientation coordinates are in the constraint subspace. The motion subspace of lower mobility manipulators may be further decomposed into
Industrial_robot
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
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
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
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
Differential geometry construct on fiber bundles
vector subspace of the tangent space T e E {\displaystyle T_{e}E} to E {\displaystyle E} at e {\displaystyle e} , called the horizontal subspace of the
Ehresmann_connection
Concepts from linear algebra
distinct eigenvalues. Any subspace spanned by eigenvectors of T is an invariant subspace of T, and the restriction of T to such a subspace is diagonalizable.
Eigenvalues_and_eigenvectors
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
Vector space in functional analysis
("non-positive") A subspace L ⊂ K {\displaystyle L\subset K} lying within K 0 {\displaystyle K_{0}} is called a neutral subspace. Similarly, a subspace lying within
Indefinite inner product space
Indefinite_inner_product_space
Field of electrical engineering
ISBN 9781108552349. Tanaka, Y.; Eldar, Y. (2020). "Generalized Sampling on Graphs with Subspace and Smoothness Prior". IEEE Transactions on Signal Processing. 68: 2272–2286
Signal_processing
Branch of mathematics
mathematical structures. These subsets are called linear subspaces. More precisely, a linear subspace of a vector space V over a field F is a subset W of V
Linear_algebra
Grouping a set of objects by similarity
also belong to the parent cluster Subspace clustering: while an overlapping clustering, within a uniquely defined subspace, clusters are not expected to overlap
Cluster_analysis
Form of radar used to create images of landscapes
signal subspace. The MUSIC method is considered to be a poor performer in SAR applications. This method uses a constant instead of the clutter subspace. In
Synthetic-aperture_radar
Unitary transformation in quantum mechanics
interacting subspaces. Using a perturbative approach, the transformation can be constructed such that the interaction between the two subspaces vanishes
Schrieffer–Wolff transformation
Schrieffer–Wolff_transformation
Vector space of infinite sequences
functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or
Sequence_space
Mathematical space with a notion of distance
topological space, then the subspace consisting of all bounded continuous functions from X to M is also complete. When X is a subspace of R n {\displaystyle
Metric_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
Number of values in the final calculation of a statistic that are free to vary
of the data vector onto the subspace spanned by the vector of 1's. The 1 degree of freedom is the dimension of this subspace. The second residual vector
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Inclusion of one mathematical structure in another, preserving properties of interest
) {\displaystyle f(X)} (where f ( X ) {\displaystyle f(X)} carries the subspace topology inherited from Y {\displaystyle Y} ). Intuitively then, the embedding
Embedding
in K span a finite-dimensional subspace. The union of all finite-dimension K-invariant subspaces is itself a subspace, and K-invariant, and consists of
K-finite
handle. Subspace weapons are a class of directed energy weapons that directly affect subspace. The weapons can produce actual tears in subspace, and are
Weapons_in_Star_Trek
Property of topological spaces
{\displaystyle A\cap K} is open in K {\displaystyle K} for every compact subspace K ⊆ X . {\displaystyle K\subseteq X.} Other definitions use a family of
Compactly_generated_space
Subset which is both open and closed
\mathbb {R} .} The topology on X {\displaystyle X} is inherited as the subspace topology from the ordinary topology on the real line R . {\displaystyle
Clopen_set
Method of data analysis
principal components, and the PCA subspace spanned by the principal directions is identical to the cluster centroid subspace. However, that PCA is a useful
Principal_component_analysis
Numerical method for solving physical or engineering problems
differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural
Finite_element_method
Method of solving differential equations
the subspace correction framework, BPX preconditioner is a parallel subspace correction method whereas the classic V-cycle is a successive subspace correction
Multigrid_method
Nonlinear equation which arises on linear optimal control problems
infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous
Algebraic_Riccati_equation
codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code
Hamming_space
Method for finding largest (or smallest) eigenvalues
{\displaystyle P^{i}} , rather than on the whole subspace. The constantly increasing amount of computer memory allows typical block sizes nowadays in the 10 3 − 10
LOBPCG
Linear map from a vector space to its field of scalars
vector subspace N {\displaystyle N} of X {\displaystyle X} such that M ⊊ N ⊊ X . {\displaystyle M\subsetneq N\subsetneq X.} A vector subspace M {\displaystyle
Linear_form
Series of crossover fighting games
mix of platforming levels and typical battles based on various game series. Brawl's was far more expansive; titled "Subspace Emissary", it was a story-based
Super_Smash_Bros.
Locally compact topological group with an invariant averaging operation
ℓ∞(Z) be the constant sequence ui = 1 for all i ∈ Z. Any element y of the subspace Y = {Sx - x : x ∈ ℓ∞(Z)} has a distance greater than or equal to 1 from
Amenable_group
Relation between sides of a right triangle
coordinate subspace. μ m p i {\displaystyle \mu _{mp_{i}}} is the measure of the m-dimensional set projection onto m-dimensional coordinate subspace i. Because
Pythagorean_theorem
Mathematical construction relating to infinite-dimensional spaces
{\displaystyle B} is a Banach space that contains H {\displaystyle H} as a dense subspace. If B {\displaystyle B} is "sufficiently larger" than H {\displaystyle
Abstract_Wiener_space
Movement of an object which leaves at least one point unchanged
These vectors span the same subspace as v {\displaystyle v} and v ¯ {\displaystyle {\bar {v}}} , which is an invariant subspace under the application of
Rotation
Superconducting qubit implementation
is to use harmonic oscillator modes, or bosonic modes, as the logical subspace. In such systems, transmons are used as ancillas for universal control
Transmon
Method used in statistics, pattern recognition, and other fields
in the derivation of the Fisher discriminant can be extended to find a subspace which appears to contain all of the class variability. This generalization
Linear_discriminant_analysis
Difficulties arising when analyzing data with many aspects ("dimensions")
Linear least squares Model order reduction Multilinear PCA Multilinear subspace learning Principal component analysis Singular value decomposition Bellman
Curse_of_dimensionality
Branch of mathematics
infinite-dimensional Banach spaces by examining their finite-dimensional subspaces and quotient spaces. John von Neumann in 1942 studied the asymptotic behavior
Asymptotic_geometry
System or list for multiple mail recipients
org. Archived from the original on January 18, 2024. kernel.org: What is subspace running? "public-inbox listing". lore.kernel.org. Archived from the original
Mailing_list
Partition of space by hyperplanes
written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual
Arrangement_of_hyperplanes
Function for integral Fourier-like transform
components. The frequency bands or subspaces (sub-bands) are scaled versions of a subspace at scale 1. This subspace in turn is in most situations generated
Wavelet
Concept in machine learning
and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e
Tensor_(machine_learning)
Line with a point at infinity added
over a field K, commonly denoted P1(K), as the set of one-dimensional subspaces of a two-dimensional K-vector space. This definition is a special instance
Projective_line
Analyzes the topology of a manifold by studying differentiable functions on that manifold
{\displaystyle p} of f {\displaystyle f} is the dimension of the largest subspace of the tangent space to M {\displaystyle M} at p {\displaystyle p} on which
Morse_theory
Direction from which a signal is received
Periodogram MUSIC SAMV Maximum likelihood ESPRIT Root MUSIC Weighted subspace fitting Method of Direction Estimation (MODE) Zhang, Qilin; Abeida, Habti;
Direction_of_arrival
Vector describing a wave; often its propagation direction
surface in special relativity may be regarded as a hypersurface (a 3D subspace) in spacetime, formed by all the events passed by the wave surface. A wavetrain
Wave_vector
Observation far apart from others in statistics and data science
detect outliers, especially in the development of linear regression models. Subspace and correlation based techniques for high-dimensional numerical data It
Outlier
Subset of artificial intelligence
sparse, meaning that the mathematical model has many zeros. Multilinear subspace learning algorithms aim to learn low-dimensional representations directly
Machine_learning
Mathematical concept in algebra
on R n {\displaystyle \mathbb {R} ^{n}} naturally determines a flag of subspaces { 0 } ⊂ ker L ⊂ ker L 2 ⊂ … ⊂ ker L q − 1 ⊂ ker L q = R n {\displaystyle
Nilpotent_matrix
Property that is not changed by mathematical transformations
invariant set under T, in which case the eigenvectors span an invariant subspace which is stable under T. When T is a screw displacement, the screw axis
Invariant_(mathematics)
Type of regular Hausdorff space
by taking point-separating initial topologies. It follows that: Every subspace of a completely regular or Tychonoff space has the same property. A nonempty
Tychonoff_space
Approximation method in quantum physics
feature of the Hartree–Fock method. The Hartree–Fock method finds its typical application in the solution of the Schrödinger equation for atoms, molecules
Hartree–Fock_method
Statistical concept
distributions to be learned. The projection of each data point to a linear subspace spanned by those vectors groups points originating from the same distribution
Mixture_model
Topological space
spaces occur abundantly in real analysis. For example, they exist as subspaces in every perfect, complete metric space. (To see this, note that in such
Cantor_space
Signal processing technique
noise subspace. After these subspaces are identified, a frequency estimation function is used to find the component frequencies from the noise subspace. The
Spectral_density_estimation
Branch of statistical computational learning theory
\ldots ,t_{n})} are in a n − 1 dimensional subspace of Rn. Take a ≠ 0, a vector that is orthogonal to this subspace. Therefore: ∑ a i > 0 a i ( f ( x i ) −
Vapnik–Chervonenkis_theory
Aspect of facial recognition software
Matrix factorization (NMF) approach to learn localized part-based subspace. That subspace is effective for super-resolving the incoming face. For further
Face_hallucination
Description in Riemannian geometry
p ) {\displaystyle K(\sigma _{p})} depends on a two-dimensional linear subspace σ p {\displaystyle \sigma _{p}} of the tangent space at a point p {\displaystyle
Sectional_curvature
Topological vector space
TVSs then the LF-space is called a strict LF-space. This means that the subspace topology induced on Xn by Xn+1 is identical to the original topology on
LF-space
Mathematical transform that expresses a function of time as a function of frequency
integral Eq.1 does not exist. However, the Fourier transform on the dense subspace L 1 ∩ L 2 ( R ) ⊂ L 2 ( R ) {\displaystyle L^{1}\cap L^{2}(\mathbb {R}
Fourier_transform
Diode that emits light from an organic compound
the Efficiency of Polariton OLEDs in and Beyond the Single-Excitation Subspace". Advanced Optical Materials. 13 (12) 2403046. arXiv:2404.04257. doi:10
OLED
real or the complex numbers. A typical example is the set X {\displaystyle X} of 2 {\displaystyle 2} -dimensional subspaces w ⊂ V {\displaystyle w\subset
Schubert_variety
Quantum error correction code
spaces, a symplectic subspace corresponds to a direct sum of Pauli algebras (i.e., encoded qubits), while an isotropic subspace corresponds to a set of
Stabilizer_code
2001 video game
Tamers: Battle Spirit Ver. 1.5. The Digital World, a computer-generated subspace that exists between all forms of digital devices, and home of the creatures
Digimon_Battle_Spirit
Indicator for how well data points fit a line or curve
giving the minimal distance from the space. The smaller model space is a subspace of the larger one, and thereby the residual of the smaller model is guaranteed
Coefficient_of_determination
Ability to perceive, infer, retain or apply information
framework, Deep Blue has the power to "steer a chessboard's future into a subspace of possibility which it labels as 'winning', despite attempts by Garry
Intelligence
Designing products to facilitate 3D printing
(PSPP) chain can be used to efficiently search an AM design subspace for the optimum point with respect to the performance of the AM structure
Design for additive manufacturing
Design_for_additive_manufacturing
Type of feedforward neural network
based on convolutional gated restricted Boltzmann machines and independent subspace analysis. Its application can be seen in text-to-video models.[citation
Convolutional_neural_network
1998 video game
technology to track ships in subspace, and had discovered that the Shivans' shield technology doesn't work in subspace, a flaw that also exists within
Descent: FreeSpace – The Great War
Descent:_FreeSpace_–_The_Great_War
Type of geometric transformation
shear transformation of the polytope's vertices. For a vector space V and subspace W, a shear fixing W translates all vectors in a direction parallel to W
Shear_mapping
Technique to solve partial differential equations
which reduces the solution search space of constrained problems to the subspace of neural network that analytically satisfies the constraints. A further
Physics-informed neural networks
Physics-informed_neural_networks
Russian naval engineer, mathematician, and memoirist (1863–1945)
In 1931 he published a paper on what is now called the Krylov subspace and Krylov subspace methods. The paper deals with eigenvalue problems, namely, with
Aleksey_Krylov
Erotic practices involving domination and sadomasochism
afterglow of orgasm. The corresponding trance-like mental state is also called subspace, for the submissive, and domspace, for the dominant. Some use body stress
BDSM
Teleportation device installed on starships in Star Trek
Hunted"). The TNG episode "Bloodlines" features a dangerous and experimental "subspace transporter" capable of interstellar distances and the Dominion had the
Transporter_(Star_Trek)
2002 American science fiction film by Stuart Baird
but is ambushed by Scimitar in the Bassen Rift, a region that prevents subspace communication. Despite the aid of two Romulan Warbirds, Enterprise is heavily
Star_Trek:_Nemesis
Result of commutative algebra
general projection from an affine space containing X to a d-dimensional subspace. More generally, in the language of schemes, the theorem can equivalently
Noether_normalization_lemma
Automated recognition of patterns and regularities in data
procedure is then to minimize the error rate (maximize the correctness) on a "typical" test set. For a probabilistic pattern recognizer, the problem is instead
Pattern_recognition
Process of "purifying" entangled quantum states
projects Bob's qubits onto a subspace P i T {\displaystyle \mathbf {P} _{i}^{T}} corresponding to Alice's projected subspace P i {\displaystyle \mathbf
Entanglement_distillation
Nonparametric spectral estimation method
frequency domain decomposition. The origins of SSA and, more generally, of subspace-based methods for signal processing, go back to the eighteenth century
Singular_spectrum_analysis
Data mining framework
HDBSCAN Mean-shift clustering BIRCH clustering SUBCLU (Density-Connected Subspace Clustering for High-Dimensional Data) CLIQUE clustering ORCLUS and PROCLUS
ELKI
1995 video game
Jagged Edge - Shiny and Grubs". Atari Explorer Online. Vol. 3, no. 13. Subspace Publishers. Archived from the original on 2016-03-03. Retrieved 2019-03-24
Earthworm_Jim_2
Vector quantization algorithm minimizing the sum of squared deviations
clusters intertwined in space do not separate well when projected onto PCA subspace. k-means should not be expected to do well on this data. It is straightforward
K-means_clustering
Loss of quantum coherence
Alternatively we can say that they occupy different lower-dimensional subspaces in the phase space of the joint system. The effective dimensionality of
Quantum_decoherence
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