nLab
linear group
Context
Group Theory
group theory
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
Linear algebra
linear algebra, higher linear algebra
Ingredients
Basic concepts
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ring, A-∞ ring
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commutative ring, E-∞ ring
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module, ∞-module, (∞,n)-module
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field, ∞-field
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vector space, 2-vector space
rational vector space
real vector space
complex vector space
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topological vector space
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linear basis,
orthogonal basis, orthonormal basis
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linear map, antilinear map
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matrix (square, invertible, diagonal, hermitian, symmetric, …)
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general linear group, matrix group
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eigenspace, eigenvalue
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inner product, Hermitian form
Gram-Schmidt process
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Hilbert space
Theorems
(…)
Contents
Definition
A group is called linear if it admits a monomorphism into a general linear group
for some dimension and some ground field , in other words: it it admits a faithful linear representation of finite-dimensional.
Properties
References
See also:
Last revised on December 29, 2025 at 12:07:21.
See the history of this page for a list of all contributions to it.