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- Lie_bracket_of_vector_fields abstract "In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator which assigns, to any two vector fields X and Y on a smooth manifold M, a third vector field denoted [X, Y]. Conceptually, the Lie bracket [X,Y] is the derivative of Y in the `direction' generated by X. It is a special case of the Lie derivative which allows to form the derivative of any tensor field in the direction generated by X. Indeed, [X,Y] equals the Lie derivative . The Lie bracket is an R-bilinear operation and turns the set of all vector fields on the manifold M into an (infinite-dimensional) Lie algebra.The Lie bracket plays an important role in differential geometry and differential topology, for instance in the Frobenius theorem, and is also fundamental in the geometric theory for nonlinear control systems (Isaiah 2009, pp. 20–21, nonholonomic systems; Khalil 2002, pp. 523–530, feedback linearization).".
- Lie_bracket_of_vector_fields wikiPageExternalLink NonlinearSystems.
- Lie_bracket_of_vector_fields wikiPageID "10282799".
- Lie_bracket_of_vector_fields wikiPageRevisionID "578925633".
- Lie_bracket_of_vector_fields hasPhotoCollection Lie_bracket_of_vector_fields.
- Lie_bracket_of_vector_fields id "p/l058550".
- Lie_bracket_of_vector_fields title "Lie bracket".
- Lie_bracket_of_vector_fields subject Category:Bilinear_operators.
- Lie_bracket_of_vector_fields subject Category:Binary_operations.
- Lie_bracket_of_vector_fields subject Category:Differential_topology.
- Lie_bracket_of_vector_fields subject Category:Riemannian_geometry.
- Lie_bracket_of_vector_fields type Abstraction100002137.
- Lie_bracket_of_vector_fields type BilinearOperators.
- Lie_bracket_of_vector_fields type Function113783816.
- Lie_bracket_of_vector_fields type MathematicalRelation113783581.
- Lie_bracket_of_vector_fields type Operator113786413.
- Lie_bracket_of_vector_fields type Relation100031921.
- Lie_bracket_of_vector_fields comment "In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator which assigns, to any two vector fields X and Y on a smooth manifold M, a third vector field denoted [X, Y]. Conceptually, the Lie bracket [X,Y] is the derivative of Y in the `direction' generated by X.".
- Lie_bracket_of_vector_fields label "Corchete de Lie (campos de vectores)".
- Lie_bracket_of_vector_fields label "Lie bracket of vector fields".
- Lie_bracket_of_vector_fields sameAs Corchete_de_Lie_(campos_de_vectores).
- Lie_bracket_of_vector_fields sameAs m.02q7bbg.
- Lie_bracket_of_vector_fields sameAs Q5478310.
- Lie_bracket_of_vector_fields sameAs Q5478310.
- Lie_bracket_of_vector_fields sameAs Lie_bracket_of_vector_fields.
- Lie_bracket_of_vector_fields wasDerivedFrom Lie_bracket_of_vector_fields?oldid=578925633.
- Lie_bracket_of_vector_fields isPrimaryTopicOf Lie_bracket_of_vector_fields.