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Vector space

In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of…

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Overview

Definition and basic properties

Bases, vector coordinates, and subspaces

History

Examples

Linear maps and matrices

Basic constructions

Vector spaces with additional structure

Related structures

Advanced semantic analysis

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Map overview Semantic statistics

Vector space

Nodes274
Edges273
Triples164
Avg. degree1.99
Density0.007299
Components1

How this topic connects Entity context

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Vector space

Top relations

related to history · 18
Vector space → Argand, Around, Bellavitis, Bolzano, Euclidean, Fermat, French, Hamilton, Laguerre, Möbius, Pierre, R2, R4, René Descartes, They, To, Vector, Vectors
related to Normed vector spaces and inner product spaces · 12
Vector space → An, Because, Coordinate, In, Lorentz, Measuring, Minkowski, Norms, Note, Singling, The, Vector
related to Vector bundles · 12
Vector space → Despite, For, In, It, K-theory, More, Möbius, Properties, S1, S2, The, Vector
related to Arrows in the plane · 9
Vector space → Another, Equivalently, Given, In, It, Moreover, The, This, When
related to Bases, vector coordinates, and subspaces · 9
Vector space → Bases, Consider, For, Hamel, In, It, One, The, They
related to Eigenvalues and eigenvectors · 9
Vector space → Any, By, Endomorphisms, Equivalently, Id, If, Jordan, The, This
related to Vector spaces with additional structure · 8
Vector space → For, From, However, Lebesgue, Likewise, Ordered, Riesz, Therefore
related to Affine and projective spaces · 7
Vector space → An, Grassmannians, If, In, More, Roughly, The
related to Modules · 7
Vector space → For, Modules, Nevertheless, Some, The, Z-module, Z/2Z
related to Topological vector spaces · 7
Vector space → Compatible, Convergence, For, In, Roughly, The, To

Important terminology Word statistics

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Important terminology

vector displaystyle space spaces mathbf linear called field vectors example functions function two also product scalar multiplication dimension given set

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Vector spaceis aabelian group under addition0.90text
Vector spaceis amodule over a field0.90text
Vector spaceis abasis if its elements are linearly independent and span the vector space0.90text
Vector spaceis aaffine space over itself0.90text
spaces of p-integrable functionsinstance ofnotably with key concepts0.80text
Hilbert spacesinstance ofnotably with key concepts0.80text
the first isomorphism theoreminstance ofmany statements0.80text
linear maps to several variablesinstance ofwhich deals with extending notions0.80text
energyinstance ofDefinite values for physical properties0.80text
or momentuminstance ofDefinite values for physical properties0.80text
correspond to eigenvalues of a certaininstance ofDefinite values for physical properties0.80text
locally free modulesinstance ofThe algebro-geometric interpretation of commutative rings via their spectrum allows the development of concepts0.80text

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    Min side: 3
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