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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
Theorem on extension of bounded linear functionals
analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space
Hahn–Banach_theorem
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
Result about when a matrix can be diagonalized
the collection of all the subspaces is then represented by a projection-valued measure. One formulation of the spectral theorem expresses the operator A
Spectral_theorem
Application of geometry in number theory
lattice points in some convex bodies. In the geometry of numbers, the subspace theorem was obtained by Wolfgang M. Schmidt in 1972. It states that if n is
Geometry_of_numbers
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
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
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Theorem in algebraic topology
excision theorem is a theorem about relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space X {\displaystyle X} and subspaces A
Excision_theorem
Describes the fundamental group in terms of a cover by two open path-connected subspaces
and in particular all pushouts. Theorem. Let the topological space X be covered by the interiors of two subspaces X1, X2 and let A be a set which meets
Seifert–Van_Kampen_theorem
Finitely many for a smooth algebraic curve of genus > 0 defined over a number field
Pietro Corvaja gave a new proof by using a new method based on the subspace theorem. Siegel's result was ineffective for g ≥ 2 {\displaystyle g\geq 2}
Siegel's theorem on integral points
Siegel's_theorem_on_integral_points
a subspace, there exists a projection from the ambient space onto c 0 {\displaystyle c_{0}} whose norm is at most 2 {\displaystyle 2} . The theorem is
Sobczyk's_theorem
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
are sequentially compact in the subspace topology – are precisely the closed and bounded subsets. This form of the theorem makes especially clear the analogy
Bolzano–Weierstrass_theorem
Milman–Pettis theorem (Banach space) Moore–Aronszajn theorem (Hilbert space) Orlicz–Pettis theorem (functional analysis) Quotient of subspace theorem (functional
List_of_theorems
Condition for a linear operator to be open
functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
Branch of mathematics
c{\sqrt[{4}]{n}}} . Quotient of subspace theorem, or Milman's M*-estimate, concerns the geometry of proportional-dimensional subspaces and quotients, showing that
Asymptotic_geometry
Algebraic numbers are not near many rationals
Diophantine equations. There is a higher-dimensional version, Schmidt's subspace theorem, of the basic result. There are also numerous extensions, for example
Roth's_theorem
In linear algebra, relation between 3 dimensions
statement of the theorem with dim V = n {\displaystyle \dim V=n} . As Ker T ⊂ V {\displaystyle \operatorname {Ker} T\subset V} is a subspace, there exists
Rank–nullity_theorem
Theorem
is a closed linear operator defined on a dense linear subspace of X. The Hille–Yosida theorem provides a necessary and sufficient condition for a closed
Hille–Yosida_theorem
Theorem used in quantum mechanics for angular momentum calculations
say that the Wigner–Eckart theorem is a theorem that tells how vector operators behave in a subspace. Within a given subspace, a component of a vector operator
Wigner–Eckart_theorem
Statement relating differentiable symmetries to conserved quantities
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law
Noether's_theorem
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Mathematical theorem in the study of analysis
a vector subspace of C[a, b] that is closed under multiplication of functions), and the content of the Weierstrass approximation theorem is that this
Stone–Weierstrass_theorem
Theorem in functional analysis
Banach–Alaoglu theorem to a weakly metrizable subspace of X {\displaystyle X} ; or, more succinctly, by applying the Eberlein–Šmulian theorem.) For example
Banach–Alaoglu_theorem
Basic result in the algebraic theory of quadratic forms, on extending isometries
between two subspaces of V then f extends to an isometry of V. Witt's theorem implies that the dimension of a maximal totally isotropic subspace (null space)
Witt's_theorem
Type of mathematical space
in the subspace topology. Compactness was formally introduced by Maurice Fréchet in 1906 in work generalizing the Bolzano–Weierstrass theorem from sets
Compact_space
Principle in quantum information theory
describing the subspaces accessible to Alice and Bob. The total state of the system is described by a density matrix σ. The goal of the theorem is to prove
No-communication_theorem
Partially unsolved problem in mathematics
2 has a non-trivial invariant subspace. The spectral theorem shows that all normal operators admit invariant subspaces. Aronszajn & Smith (1954) proved
Invariant_subspace_problem
Concerns the decomposition of representations of a finite group into irreducible pieces
In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations
Maschke's_theorem
Theorem of quantum information theory
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot
No-hiding_theorem
Theorem in transcendental number theory
Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem—if α1
Lindemann–Weierstrass_theorem
Branch of mathematics that studies dynamical systems
theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which
Ergodic_theory
Theorem in functional analysis
orthogonal projection P onto a subspace of dimension m such that PAP* = B. The Cauchy interlacing theorem states: Theorem. If the eigenvalues of A are α1
Min-max_theorem
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
"Small" subset of a topological space
(1): 174–179. doi:10.4064/sm-3-1-174-179. Willard 2004, Theorem 25.5. "Are proper linear subspaces of Banach spaces always meager?". "Research problems"
Meagre_set
Mathematical result on systems of linear equations
k < i. This means that si is in the linear subspace of Qm spanned by the set of the cj's. Folkman's theorem, the statement that there exist arbitrarily
Rado's theorem (Ramsey theory)
Rado's_theorem_(Ramsey_theory)
Theorem on eigenvalues and eigenvectors of Hermitian matrices
of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The theorem is named after Henri Poincaré. More specifically,
Poincaré_separation_theorem
Theorem in string theory
background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem describing properties of a functor that quantizes
Goddard–Thorn_theorem
On the number of common zeros of Laurent polynomials
different proofs of this theorem. Let A {\displaystyle A} be a finite subset of Z n . {\displaystyle \mathbb {Z} ^{n}.} Consider the subspace L A {\displaystyle
Bernstein–Kushnirenko_theorem
subspace of C0([0, 1], R), the space of all continuous functions from the unit interval into the real line. On the one hand, the Banach–Mazur theorem
Banach–Mazur_theorem
Property of artificial neural networks
In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate
Universal approximation theorem
Universal_approximation_theorem
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
In mathematics, the Lumer–Phillips theorem, named after Günter Lumer and Ralph Phillips, is a result in the theory of strongly continuous semigroups that
Lumer–Phillips_theorem
Theorem about the dual of a Hilbert space
}}x\in X\,\},} which is always a closed vector subspace of H . {\displaystyle H.} The Hilbert projection theorem guarantees that for any nonempty closed convex
Riesz_representation_theorem
Russian-American mathematician (1946–2018)
T has a non-trivial invariant subspace. Lomonosov has also published on the Bishop–Phelps theorem and Burnside's Theorem. Lomonosov received his master's
Victor_Lomonosov
Unconditionally convergent series converge absolutely
that the set of possible sums forms a real affine subspace. Extensions of the Lévy–Steinitz theorem to series in infinite-dimensional spaces have been
Riemann_series_theorem
On the approximate structure of sets whose sumset is small
In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose
Freiman's_theorem
Concept in differential geometry
closely related to the curvature of the connection, via the Ambrose–Singer theorem. The study of Riemannian holonomy has led to a number of important developments
Holonomy
the theorem on complete reducibility: the case where a representation V {\displaystyle V} contains a nontrivial, irreducible, invariant subspace W {\displaystyle
Weyl's theorem on complete reducibility
Weyl's_theorem_on_complete_reducibility
on the dimension of the subspace in Dvoretzky's theorem can be significantly improved, if one is willing to accept a subspace that is close either to
Dvoretzky's_theorem
Euclidean space without distance and angles
Quillen–Suslin theorem implies that every algebraic vector bundle over an affine space is trivial. Affine hull – Smallest affine subspace that contains
Affine_space
German mathematician
p-adic generalization of the subspace theorem of Wolfgang M. Schmidt. Schlickewei's theorem implies the Thue-Siegel-Roth theorem, whose p-adic analogue was
Hans_Peter_Schlickewei
Topics referred to by the same term
Schmidt's theorem may refer to: Krull–Schmidt theorem Wolfgang M. Schmidt's subspace theorem This disambiguation page lists mathematics articles associated
Schmidt's_theorem
Theorem
In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring,[when?] is a result
Stinespring_dilation_theorem
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
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
generated by v. The concept of a cyclic subspace is a basic component in the formulation of the cyclic decomposition theorem in linear algebra. Let T : V → V
Cyclic_subspace
Theorem stating that pointwise boundedness implies uniform boundedness
Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered
Uniform_boundedness_principle
Type of vector space in math
the Pythagorean theorem and parallelogram law hold in a Hilbert space. At a deeper level, perpendicular projection onto a linear subspace plays a significant
Hilbert_space
Upper bound on intersecting set families
following: There is a q-analog of the Erdős–Ko–Rado theorem for intersecting families of linear subspaces over finite fields. If S {\displaystyle {\mathcal
Erdős–Ko–Rado_theorem
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)
In field theory, Steinitz's theorem states that a finite extension of fields L / K {\displaystyle L/K} is simple if and only if there are only finitely
Steinitz's theorem (field theory)
Steinitz's_theorem_(field_theory)
Theorem in measure theory
In the mathematical field of mathematical analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an
Lusin's_theorem
y-x\in K.} M. Riesz extension theorem—Let E {\displaystyle E} be a real vector space, F ⊂ E {\displaystyle F\subset E} a subspace, and K ⊂ E {\displaystyle
M._Riesz_extension_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)
Locally convex topological vector space that is also a complete metric space
presence of K N {\displaystyle \mathbb {K} ^{\mathbb {N} }} as a subspace. Theorem—Let X {\displaystyle X} be a Fréchet space over the field K . {\displaystyle
Fréchet_space
On when a family of real, continuous functions has a uniformly convergent subsequence
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence
Arzelà–Ascoli_theorem
Italian mathematician (born 1957)
2002 gave a new proof of Siegel's theorem on integral points by using a new method based upon the subspace theorem. Zannier was an Invited Speaker at
Umberto_Zannier
Number of solutions of linear systems in terms of matrix ranks
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented
Rouché–Capelli_theorem
Topological space that is homeomorphic to a metric space
theorem see the Bing metrization theorem. Separable metrizable spaces can also be characterized as those spaces which are homeomorphic to a subspace of
Metrizable_space
that the analytic and algebraic special sets are equal. Subspace theorem Schmidt's subspace theorem shows that points of small height in projective space
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
In mathematics, the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Statistical theorem
In statistics, Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals
Wilks'_theorem
Theorem in mathematics
mathematics, the Beurling–Lax theorem is a theorem due to Beurling (1948) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space H
Beurling–Lax_theorem
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
contains D as an open subspace because for each z in D there is a maximal ideal consisting of functions f with f(z) = 0. The subspace D cannot make up the
Corona_theorem
usually denoted by ρ(V). The Hodge index theorem says that the subspace spanned by H in D has a complementary subspace on which the intersection pairing is
Hodge_index_theorem
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
Mathematical theorem
In mathematics, the Babuška–Lax–Milgram theorem is a generalization of the famous Lax–Milgram theorem, which gives conditions under which a bilinear form
Babuška–Lax–Milgram_theorem
Theorem in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_theorem
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)
Basic result in harmonic analysis on compact topological groups
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are
Peter–Weyl_theorem
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
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
Gives the rank of the group of units in the ring of algebraic integers of a number field
r-dimensional subspace of R r + 1 {\displaystyle \mathbb {R} ^{r+1}} consisting of all vectors whose entries have sum 0, and by Dirichlet's unit theorem the image
Dirichlet's_unit_theorem
Metric geometry
This is a generalization of the Heine–Borel theorem, which states that any closed and bounded subspace S {\displaystyle S} of R n {\displaystyle \mathbb
Complete_metric_space
translate of a linear subspace (i.e., a set of the form v + M, where v is a given vector and M is a linear subspace). Riemann series theorem Lévy, Paul (1905)
Lévy–Steinitz_theorem
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
On closed convex subsets in Hilbert space
b=c,} which proves the theorem. ◼ {\displaystyle \blacksquare } Proposition—If C {\displaystyle C} is a closed vector subspace of a Hilbert space H {\displaystyle
Hilbert_projection_theorem
Theorem representing a solvable Lie algebra
In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero, if π :
Lie's_theorem
Mathematical theorem
In mathematics, Solèr's theorem is a result concerning certain infinite-dimensional vector spaces. It states that any orthomodular form that has an infinite
Solèr's_theorem
Matrix decomposition
respectively, of M {\displaystyle \mathbf {M} } . By the rank–nullity theorem, these subspaces cannot have the same dimension if m ≠ n {\displaystyle m\neq
Singular_value_decomposition
Decomposition of periodic functions
291. Oppenheim & Schafer 2010, p. 55. "Characterizations of a linear subspace associated with Fourier series". MathOverflow. 2010-11-19. Retrieved 2014-08-08
Fourier_series
Mathematical functions that quantify complexity
distinguish some objects based on their complexity. For instance, the subspace theorem proved by Wolfgang M. Schmidt (1972) demonstrates that points of small
Height_function
Algebraic structure in linear algebra
{\displaystyle \mathbf {C} } ). The fundamental Hahn–Banach theorem is concerned with separating subspaces of appropriate topological vector spaces by continuous
Vector_space
The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven
Non-squeezing_theorem
Geometric theorem
The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists
Banach–Tarski_paradox
Theorem in the mathematical formulation of quantum mechanics
Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical
Wigner's_theorem
mathematics, specifically functional analysis, the von Neumann bicommutant theorem relates the closure of a set of bounded operators on a Hilbert space in
Von Neumann bicommutant theorem
Von_Neumann_bicommutant_theorem
Metatheorem in mathematical logic
deduction theorem fails. Most notably, the deduction theorem fails to hold in Birkhoff–von Neumann quantum logic, because the linear subspaces of a Hilbert
Deduction_theorem
SUBSPACE THEOREM
SUBSPACE THEOREM
Surname or Lastname
English (also present in Ireland)
English (also present in Ireland) : from Middle English peni, peny ‘penny’, applied as a nickname, possibly for a person of some substance or for a tenant who paid a rent of one penny. This was the common Germanic unit of value when money was still an unusual phenomenon. It was the only unit of coinage in England until the early 14th century, when the groat and the gold noble were introduced, and was a silver coin of considerable value. There is some evidence that the word was used in Old English times as a byname.
Female
English
English name derived from the vocabulary word, AMBER means "amber," the gem or color. Actually the word is of Arabic origin, from anbargris (ambergris), which refers to an oily, perfumed substance (used in making perfumes) secreted by the sperm whale.
Surname or Lastname
English
English : status name from Middle English knyghte ‘knight’, Old English cniht ‘boy’, ‘youth’, ‘serving lad’. This word was used as a personal name before the Norman Conquest, and the surname may in part reflect a survival of this. It is also possible that in a few cases it represents a survival of the Old English sense into Middle English, as an occupational name for a domestic servant. In most cases, however, it clearly comes from the more exalted sense that the word achieved in the Middle Ages. In the feudal system introduced by the Normans the word was applied at first to a tenant bound to serve his lord as a mounted soldier. Hence it came to denote a man of some substance, since maintaining horses and armor was an expensive business. As feudal obligations became increasingly converted to monetary payments, the term lost its precise significance and came to denote an honorable estate conferred by the king on men of noble birth who had served him well. Knights in this last sense normally belonged to ancient noble families with distinguished family names of their own, so that the surname is more likely to have been applied to a servant in a knightly house or to someone who had played the part of a knight in a pageant or won the title in some contest of skill.Irish : part translation of Gaelic Mac an Ridire ‘son of the rider or knight’. See also McKnight.
Male
Hebrew
(Greek Ἀμήν, Hebrew: ×ָמֵן): Greek and Hebrew name AMEN means "truly, so be it, verily." It was a custom which passed over from the synagogues into the Christian assemblies, that when he who had offered up a prayer to God, the others in attendance responded Amen, and thus made the substance of what was uttered their own.Â
Girl/Female
Hindu, Indian
Donated Substance
Boy/Male
Indian, Sanskrit
The Substance; Divine
SUBSPACE THEOREM
SUBSPACE THEOREM
Girl/Female
Muslim
Gentle (Name of the daughter of the prophet (SAW))
Boy/Male
English
Like God
Boy/Male
Hindu, Indian, Telugu, Traditional
Leader of All the Celestial Bodies
Girl/Female
Hindu
Silk
Boy/Male
Indian
Soft hearted, Tenderness of
Girl/Female
Indian
Boy/Male
Australian, Celtic, Christian, Gaelic, Irish
Lordly; Regal; Little Lord
Boy/Male
Tamil
Surname or Lastname
English (Norfolk)
English (Norfolk) : nickname from a reduced form of Middle English apostel ‘apostle’ (Old English apostol, via Latin from Greek apostolos ‘messenger’, ‘delegate’, from apostellein ‘to dispatch’). As a nickname, this may have been used for someone who had played the part of one of the twelve apostles in a play or pageant. However, the word was also used as a personal name. Compare Postlethwait.
Boy/Male
Indian, Sanskrit
Delighted
SUBSPACE THEOREM
SUBSPACE THEOREM
SUBSPACE THEOREM
SUBSPACE THEOREM
SUBSPACE THEOREM
n.
Constituent substance.
n.
That which underlies all outward manifestations; substratum; the permanent subject or cause of phenomena, whether material or spiritual; that in which properties inhere; that which is real, in distinction from that which is apparent; the abiding part of any existence, in distinction from any accident; that which constitutes anything what it is; real or existing essence.
n.
Any spongelike substance.
n.
A paramagnetic substance.
n.
The most important element in any existence; the characteristic and essential components of anything; the main part; essential import; purport.
n.
A cauterizing substance.
n.
Form without substance.
n.
A haloid substance.
v. t.
To furnish or endow with substance; to supply property to; to make rich.
n.
A crystalline substance.
n.
A divisible substance.
n.
A semifluid substance.
n.
Same as Hypostasis, 2.
n.
Body; matter; material of which a thing is made; hence, substantiality; solidity; firmness; as, the substance of which a garment is made; some textile fabrics have little substance.
n.
Surface; body; substance.
n.
A phosphorescent substance.
a.
Detached from substance.
n.
An idioelectric substance.
n.
Material possessions; estate; property; resources.