- a
bivector, as is any sum of
bivectors. Not all
bivectors can be
expressed as an
exterior product without such summation. More precisely, a
bivector that...
- six-dimensional
bivectors in four dimensions.
These can be
written Λ 2 R 4 {\displaystyle \Lambda ^{2}\mathbb {R} ^{4}} for the set of
bivectors in Euclidean...
- to lines, so are
bivectors to planes. So
every plane (in any dimension) can be ****ociated with a
bivector, and
every simple bivector is ****ociated with...
-
Lorentz group can be
considered to be that of
bivectors under commutation. [...] The Lie
algebra of
bivectors is
essentially that of
complex 3-vectors, with...
- (sometimes
called the
field strength tensor,
Faraday tensor or
Maxwell bivector) is a
mathematical object that
describes the
electromagnetic field in spacetime...
-
vectors are multiplied.
Bivectors are
connected to pseudovectors, and are used to
represent rotations in
geometric algebra. As
bivectors are
elements of a vector...
- of a
bivector and vector. In
three dimensions bivectors are dual to
vectors so the
product is
equivalent to the
cross product, with the
bivector instead...
- numbers. In this
interpretation points, vectors, and sums of
scalars and
bivectors are all
distinct types of
geometric objects. More generally, in the geometric...
- a
unique smooth bivector field π ∈ X 2 ( M ) {\displaystyle \pi \in {\mathfrak {X}}^{2}(M)} . Conversely,
given any
smooth bivector field π {\displaystyle...
-
classification of
electromagnetic fields is a
pointwise classification of
bivectors at each
point of a
Lorentzian manifold. It is used in the
study of solutions...
