The electromagnetic field tensor is another second order antisymmetric tensor field, with six components : three for the electric field and another three for the magnetic field.
12.
This can be achieved by replacing the cross product by the exterior product in the language of exterior algebra, and angular momentum becomes a contravariant second order antisymmetric tensor
13.
There's more that could be said about antisymmetric tensors, but I'll leave it at that .-- talk ) 06 : 00, 11 August 2010 ( UTC)
14.
Which is only valid in three dimensions, or an antisymmetric tensor field of second order via antisymmetrization of indices, indicated by delimiting the antisymmetrized indices by square brackets ( see Ricci calculus ):
15.
Where \ omega _ { ij } is the average angular velocity of the rotating particles ( as an antisymmetric tensor rather than a pseudovector ) and \ eta _ r is the rotational viscosity coefficient.
16.
In three dimensions antisymmetric tensors of rank 0, 1, 2, 3 have 1, 3, 3, 1 components respectively, and they are scalars, vectors, pseudovectors, and pseudoscalars respectively.
17.
In differential geometry, a " "'p "-vector "'is the antisymmetric tensor obtained by taking linear combinations of the wedge product of " p " tangent vectors, for some integer.
18.
The angular momentum of a classical pointlike particle orbiting about an axis, defined by "'x "'?"'p "'} }, is another example of a pesudovector, with corresponding antisymmetric tensor:
19.
An example of a four dimensional second order antisymmetric tensor is the relativistic angular momentum, which has six components : three are the classical angular momentum, and the other three are related to the boost of the center of mass of the system.
20.
In the-entry of the table, " M " denotes the dimensionality of the underlying vector space or manifold because for each dimension of the space, a separate index is needed to select that dimension to get a maximally covariant antisymmetric tensor.
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