wedge product
Exterior algebra operation
The wedge product is an operation in mathematics that combines vectors or differential forms to produce new objects of higher dimension.
Two vectors wedge together to give an oriented area; three give an oriented volume.
The wedge product is antisymmetric: swapping the order reverses the sign.
The wedge product of dx and dy gives the area element dx ∧ dy.
Central to differential geometry and physics, it generalizes the cross product to any number of dimensions.
Negated when transposed
- bilinearLinear in both arguments
- alternatingOccurring in turns
- Clifford algebraAlgebra from quadratic forms
- basisUnderlying support or principle
Extent of surface
- volumeAmount of space filled
- orientationPosition relative to surroundings
- parallelogramQuadrilateral with paired parallels
- parallelepipedSix-faced solid, parallelogram sides
simplex · determinant · span · projection · magnitude · direction · right-hand rule
Many and various
- integrationCombining into a whole
- pullbackWithdrawal or reduction
- covariantChanging correspondingly under transformation
Symbol marking insertions
- index notationSymbolic component addressing system
- permutationArrangement in specific order
- signMark conveying information
- contractionReduction in size
antisymmetric
Negated when transposed
- bilinearLinear in both arguments
- alternatingOccurring in turns
- Clifford algebraAlgebra from quadratic forms
area
Extent of surface
- volumeAmount of space filled
- orientationPosition relative to surroundings
- parallelogramQuadrilateral with paired parallels
parallelepiped · simplex · determinant · span · projection · magnitude · direction · right-hand rule
manifold
Many and various
- integrationCombining into a whole
- pullbackWithdrawal or reduction
- covariantChanging correspondingly under transformation
caret
Symbol marking insertions
- index notationSymbolic component addressing system
- permutationArrangement in specific order
- signMark conveying information
- Hypercomplex Mathquaternion, Clifford algebra, rotor, rotors, blade
- geometryangles, circles, angle, shapes, lines
- tensorstensors, index notation, covariant, contraction, valence