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General linear group

In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the…

Products, As a Lie group/algebra & Related groups and monoids

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Overview

General linear group of a vector space

In terms of determinants

As a Lie group/algebra

Over finite fields

Special linear group

Other subgroups

Related groups and monoids

Infinite general linear group

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Map overview Semantic statistics

General linear group

Nodes136
Edges135
Triples38
Avg. degree1.99
Density0.014706
Components1

How this topic connects Entity context

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General linear group

Top relations

related to External links · 10
General linear group → Acting, Ed Pegg, EMS Press, Encyclopedia, General, GL, Jr, Mathematics, Points, Wolfram Demonstrations Project
related to Complex case · 6
General linear group → As, Complex, GL, Lie, The, These
related to Infinite general linear group · 6
General linear group → Bott, GL, It, K-theory, K1, The
related to Real case · 6
General linear group → GL, Lie, The, The Lie, To, Zariski
related to General linear group of a vector space · 5
General linear group → Aut, Given, GL, If, The
related to history · 4
General linear group → Chevalier, Galois, GL, The
is a · 1
General linear group → direct limit of the inclusions GL

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Important terminology

displaystyle group operatorname gl linear matrices mathbb general matrix invertible determinant times field lie sl set also special subgroup isomorphic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
General linear groupis adirect limit of the inclusions GL0.90text
General linear grouprelated to Complex caseThe0.60section
General linear grouprelated to Complex caseGL0.60section
General linear grouprelated to Complex caseLie0.60section
General linear grouprelated to Complex caseAs0.60section
General linear grouprelated to Complex caseThese0.60section
General linear grouprelated to Complex caseComplex0.60section
General linear grouprelated to External linksGeneral0.60section
General linear grouprelated to External linksEncyclopedia0.60section
General linear grouprelated to External linksMathematics0.60section
General linear grouprelated to External linksEMS Press0.60section
General linear grouprelated to External linksGL0.60section

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