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- General_linear_group abstract "In mathematics, the general linear group of degree n is the set of n×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. The group is so named because the columns of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position.To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix. For example, the general linear group over R (the set of real numbers) is the group of n×n invertible matrices of real numbers, and is denoted by GLn(R) or GL(n, R).More generally, the general linear group of degree n over any field F (such as the complex numbers), or a ring R (such as the ring of integers), is the set of n×n invertible matrices with entries from F (or R), again with matrix multiplication as the group operation. Typical notation is GLn(F) or GL(n, F), or simply GL(n) if the field is understood.More generally still, the general linear group of a vector space GL(V) is the abstract automorphism group, not necessarily written as matrices.The special linear group, written SL(n, F) or SLn(F), is the subgroup of GL(n, F) consisting of matrices with a determinant of 1.The group GL(n, F) and its subgroups are often called linear groups or matrix groups (the abstract group GL(V) is a linear group but not a matrix group). These groups are important in the theory of group representations, and also arise in the study of spatial symmetries and symmetries of vector spaces in general, as well as the study of polynomials. The modular group may be realised as a quotient of the special linear group SL(2, Z).If n ≥ 2, then the group GL(n, F) is not abelian.".
- General_linear_group wikiPageExternalLink GL2PAndGL33ActingOnPoints.
- General_linear_group wikiPageID "113564".
- General_linear_group wikiPageLength "21223".
- General_linear_group wikiPageOutDegree "156".
- General_linear_group wikiPageRevisionID "676367140".
- General_linear_group wikiPageWikiLink Abelian_group.
- General_linear_group wikiPageWikiLink Affine_group.
- General_linear_group wikiPageWikiLink Affine_space.
- General_linear_group wikiPageWikiLink Affine_transformation.
- General_linear_group wikiPageWikiLink Algebraic_K-theory.
- General_linear_group wikiPageWikiLink Algebraic_variety.
- General_linear_group wikiPageWikiLink Alternating_form.
- General_linear_group wikiPageWikiLink Automorphism.
- General_linear_group wikiPageWikiLink Automorphism_group.
- General_linear_group wikiPageWikiLink Basis_(linear_algebra).
- General_linear_group wikiPageWikiLink Betti_number.
- General_linear_group wikiPageWikiLink Bijection.
- General_linear_group wikiPageWikiLink Bijective.
- General_linear_group wikiPageWikiLink Bilinear_form.
- General_linear_group wikiPageWikiLink Block_matrix.
- General_linear_group wikiPageWikiLink Bott_periodicity.
- General_linear_group wikiPageWikiLink Bott_periodicity_theorem.
- General_linear_group wikiPageWikiLink Category:Abstract_algebra.
- General_linear_group wikiPageWikiLink Category:Lie_groups.
- General_linear_group wikiPageWikiLink Category:Linear_algebra.
- General_linear_group wikiPageWikiLink Center_(group_theory).
- General_linear_group wikiPageWikiLink Center_of_a_group.
- General_linear_group wikiPageWikiLink Characteristic_(algebra).
- General_linear_group wikiPageWikiLink Classical_group.
- General_linear_group wikiPageWikiLink Collineation.
- General_linear_group wikiPageWikiLink Collineation_group.
- General_linear_group wikiPageWikiLink Commutative_ring.
- General_linear_group wikiPageWikiLink Commutator.
- General_linear_group wikiPageWikiLink Compact_space.
- General_linear_group wikiPageWikiLink Complex_number.
- General_linear_group wikiPageWikiLink Connected_space.
- General_linear_group wikiPageWikiLink Degenerate_bilinear_form.
- General_linear_group wikiPageWikiLink Determinant.
- General_linear_group wikiPageWikiLink Diagonal_matrix.
- General_linear_group wikiPageWikiLink Differentiable_manifold.
- General_linear_group wikiPageWikiLink Dimension_(vector_space).
- General_linear_group wikiPageWikiLink Direct_limit.
- General_linear_group wikiPageWikiLink Direct_limit_of_groups.
- General_linear_group wikiPageWikiLink Ed_Pegg,_Jr..
- General_linear_group wikiPageWikiLink Empty_set.
- General_linear_group wikiPageWikiLink Exterior_algebra.
- General_linear_group wikiPageWikiLink Fano_plane.
- General_linear_group wikiPageWikiLink Field_(mathematics).
- General_linear_group wikiPageWikiLink Field_automorphism.
- General_linear_group wikiPageWikiLink Field_with_one_element.
- General_linear_group wikiPageWikiLink Finite_field.
- General_linear_group wikiPageWikiLink First_isomorphism_theorem.
- General_linear_group wikiPageWikiLink Free_module.
- General_linear_group wikiPageWikiLink Fundamental_group.
- General_linear_group wikiPageWikiLink Galois_group.
- General_linear_group wikiPageWikiLink General_linear_position.
- General_linear_group wikiPageWikiLink General_position.
- General_linear_group wikiPageWikiLink General_semilinear_group.
- General_linear_group wikiPageWikiLink Grassmannian.
- General_linear_group wikiPageWikiLink Group_(mathematics).
- General_linear_group wikiPageWikiLink Group_action.
- General_linear_group wikiPageWikiLink Group_center.
- General_linear_group wikiPageWikiLink Group_extension.
- General_linear_group wikiPageWikiLink Group_homomorphism.
- General_linear_group wikiPageWikiLink Group_isomorphism.
- General_linear_group wikiPageWikiLink Group_representation.
- General_linear_group wikiPageWikiLink Hamel_dimension.
- General_linear_group wikiPageWikiLink Hermitian_form.
- General_linear_group wikiPageWikiLink Hilbert_space.
- General_linear_group wikiPageWikiLink Identity_component.
- General_linear_group wikiPageWikiLink Identity_matrix.
- General_linear_group wikiPageWikiLink Inner_automorphism.
- General_linear_group wikiPageWikiLink Inner_automorphism_group.
- General_linear_group wikiPageWikiLink Integer.
- General_linear_group wikiPageWikiLink Inverse_element.
- General_linear_group wikiPageWikiLink Invertible.
- General_linear_group wikiPageWikiLink Invertible_matrix.
- General_linear_group wikiPageWikiLink Isomorphic.
- General_linear_group wikiPageWikiLink Isomorphism.
- General_linear_group wikiPageWikiLink Isomorphism_theorem.
- General_linear_group wikiPageWikiLink Kernel_(algebra).
- General_linear_group wikiPageWikiLink Kuipers_theorem.
- General_linear_group wikiPageWikiLink Lie_algebra.
- General_linear_group wikiPageWikiLink Lie_group.
- General_linear_group wikiPageWikiLink Lie_subgroup.
- General_linear_group wikiPageWikiLink Linear_complex_structure.
- General_linear_group wikiPageWikiLink Linear_independence.
- General_linear_group wikiPageWikiLink Linear_map.
- General_linear_group wikiPageWikiLink Linear_span.
- General_linear_group wikiPageWikiLink Linear_transformation.
- General_linear_group wikiPageWikiLink Linearly_independent.
- General_linear_group wikiPageWikiLink List_of_finite_simple_groups.
- General_linear_group wikiPageWikiLink Lorentz_group.
- General_linear_group wikiPageWikiLink Mathematics.
- General_linear_group wikiPageWikiLink Matrix_multiplication.
- General_linear_group wikiPageWikiLink Matrix_ring.
- General_linear_group wikiPageWikiLink Maximal_compact_subgroup.
- General_linear_group wikiPageWikiLink Modular_group.
- General_linear_group wikiPageWikiLink Monoid.