Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Symplectic_vector_space> ?p ?o }
- Symplectic_vector_space abstract "In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form.A symplectic bilinear form is a bilinear form: a map ω : V × V → F that is bilinear (i.e. linear in each argument separately), alternating: ω(v, v) = 0 holds for all v ∈ V, and nondegenerate: ω(u, v) = 0 for all v ∈ V implies that u is zero.If the underlying field has characteristic not 2, alternation is equivalent to skew-symmetry. If the characteristic is 2, the skew-symmetry is implied by, but does not imply alternation. In this case every symplectic form is a symmetric form, but not vice versa. Working in a fixed basis, ω can be represented by a matrix. The conditions above say that this matrix must be skew-symmetric, nonsingular, and hollow. This is not the same thing as a symplectic matrix, which represents a symplectic transformation of the space. If V is finite-dimensional, then its dimension must necessarily be even since every skew-symmetric, hollow matrix of odd size has determinant zero. Notice the condition that the matrix be hollow is not redundant if the characteristic of the field is 2. A symplectic form behaves quite differently from a symmetric form, for example, the scalar product on Euclidean vector spaces.".
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- Symplectic_vector_space wikiPageRevisionID "665052528".
- Symplectic_vector_space wikiPageWikiLink Almost_complex_manifold.
- Symplectic_vector_space wikiPageWikiLink Almost_complex_structure.
- Symplectic_vector_space wikiPageWikiLink Alternating_product.
- Symplectic_vector_space wikiPageWikiLink Basis_(linear_algebra).
- Symplectic_vector_space wikiPageWikiLink Bilinear_form.
- Symplectic_vector_space wikiPageWikiLink Block_matrix.
- Symplectic_vector_space wikiPageWikiLink Canonical_commutation_relation.
- Symplectic_vector_space wikiPageWikiLink Canonical_coordinate.
- Symplectic_vector_space wikiPageWikiLink Canonical_coordinates.
- Symplectic_vector_space wikiPageWikiLink Category:Bilinear_forms.
- Symplectic_vector_space wikiPageWikiLink Category:Linear_algebra.
- Symplectic_vector_space wikiPageWikiLink Category:Symplectic_geometry.
- Symplectic_vector_space wikiPageWikiLink Central_extension_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Characteristic_(algebra).
- Symplectic_vector_space wikiPageWikiLink Codimension.
- Symplectic_vector_space wikiPageWikiLink Complexification.
- Symplectic_vector_space wikiPageWikiLink Contravariant_functor.
- Symplectic_vector_space wikiPageWikiLink Cotangent_bundle.
- Symplectic_vector_space wikiPageWikiLink Deformation_quantization.
- Symplectic_vector_space wikiPageWikiLink Degenerate_bilinear_form.
- Symplectic_vector_space wikiPageWikiLink Determinant.
- Symplectic_vector_space wikiPageWikiLink Differentiable_manifold.
- Symplectic_vector_space wikiPageWikiLink Dimension_(vector_space).
- Symplectic_vector_space wikiPageWikiLink Direct_sum_of_modules.
- Symplectic_vector_space wikiPageWikiLink Direct_sum_of_vector_spaces.
- Symplectic_vector_space wikiPageWikiLink Dual_space.
- Symplectic_vector_space wikiPageWikiLink Even_number.
- Symplectic_vector_space wikiPageWikiLink Exterior_algebra.
- Symplectic_vector_space wikiPageWikiLink Field_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Finite-dimensional.
- Symplectic_vector_space wikiPageWikiLink Functor.
- Symplectic_vector_space wikiPageWikiLink Gram–Schmidt_process.
- Symplectic_vector_space wikiPageWikiLink Group_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Group_algebra.
- Symplectic_vector_space wikiPageWikiLink Group_extension.
- Symplectic_vector_space wikiPageWikiLink Group_representation.
- Symplectic_vector_space wikiPageWikiLink Heisenberg_group.
- Symplectic_vector_space wikiPageWikiLink Hollow_matrix.
- Symplectic_vector_space wikiPageWikiLink Identity_matrix.
- Symplectic_vector_space wikiPageWikiLink If_and_only_if.
- Symplectic_vector_space wikiPageWikiLink Invertible_matrix.
- Symplectic_vector_space wikiPageWikiLink Jerrold_E._Marsden.
- Symplectic_vector_space wikiPageWikiLink Lagrangian_Grassmannian.
- Symplectic_vector_space wikiPageWikiLink Lie_algebra.
- Symplectic_vector_space wikiPageWikiLink Lie_group.
- Symplectic_vector_space wikiPageWikiLink Linear_complex_structure.
- Symplectic_vector_space wikiPageWikiLink Linear_map.
- Symplectic_vector_space wikiPageWikiLink Linear_subspace.
- Symplectic_vector_space wikiPageWikiLink Linear_transformation.
- Symplectic_vector_space wikiPageWikiLink Maslov_index.
- Symplectic_vector_space wikiPageWikiLink Mathematics.
- Symplectic_vector_space wikiPageWikiLink Matrix_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Momentum_operator.
- Symplectic_vector_space wikiPageWikiLink Nondegenerate_form.
- Symplectic_vector_space wikiPageWikiLink Nonsingular_matrix.
- Symplectic_vector_space wikiPageWikiLink Orientation_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Orientation_(vector_space).
- Symplectic_vector_space wikiPageWikiLink Orthogonal_complement.
- Symplectic_vector_space wikiPageWikiLink Parity_(mathematics).
- Symplectic_vector_space wikiPageWikiLink Position_operator.
- Symplectic_vector_space wikiPageWikiLink Pullback_(differential_geometry).
- Symplectic_vector_space wikiPageWikiLink Quotient_space_(linear_algebra).
- Symplectic_vector_space wikiPageWikiLink Ralph_Abraham.
- Symplectic_vector_space wikiPageWikiLink Real_subspace.
- Symplectic_vector_space wikiPageWikiLink Reality_structure.
- Symplectic_vector_space wikiPageWikiLink Skew-symmetric_matrix.
- Symplectic_vector_space wikiPageWikiLink Smooth_manifold.
- Symplectic_vector_space wikiPageWikiLink Stone–von_Neumann_theorem.
- Symplectic_vector_space wikiPageWikiLink Symmetric_algebra.
- Symplectic_vector_space wikiPageWikiLink Symmetric_bilinear_form.
- Symplectic_vector_space wikiPageWikiLink Symmetric_form.
- Symplectic_vector_space wikiPageWikiLink Symplectic_basis.
- Symplectic_vector_space wikiPageWikiLink Symplectic_group.
- Symplectic_vector_space wikiPageWikiLink Symplectic_manifold.
- Symplectic_vector_space wikiPageWikiLink Symplectic_matrix.
- Symplectic_vector_space wikiPageWikiLink Symplectic_representation.
- Symplectic_vector_space wikiPageWikiLink Tangent_bundle.
- Symplectic_vector_space wikiPageWikiLink Tangent_space.
- Symplectic_vector_space wikiPageWikiLink Vector_space.
- Symplectic_vector_space wikiPageWikiLink Volume_form.
- Symplectic_vector_space wikiPageWikiLink Weyl_algebra.
- Symplectic_vector_space wikiPageWikiLink Wigner–Weyl_transform.
- Symplectic_vector_space wikiPageWikiLinkText "Darboux basis".
- Symplectic_vector_space wikiPageWikiLinkText "Hamiltonian".
- Symplectic_vector_space wikiPageWikiLinkText "Symplectic vector space".
- Symplectic_vector_space wikiPageWikiLinkText "isotropic".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic basis".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic form".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic forms".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic structure".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic vector space".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic vector spaces".
- Symplectic_vector_space wikiPageWikiLinkText "symplectic".
- Symplectic_vector_space hasPhotoCollection Symplectic_vector_space.
- Symplectic_vector_space wikiPageUsesTemplate Template:Further.