- In mathematics, a
bivector or 2-vector is a
quantity in
exterior algebra or
geometric algebra that
extends the idea of
scalars and vectors. Considering...
- a
unique smooth bivector field π ∈ X 2 ( M ) {\displaystyle \pi \in {\mathfrak {X}}^{2}(M)} . Conversely,
given any
smooth bivector field π {\displaystyle...
- a
bivector is the
vector part of a biquaternion. For
biquaternion q = w + xi + yj + zk, w is
called the
biscalar and xi + yj + zk is its
bivector part...
- 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...
- (sometimes
called the
field strength tensor,
Faraday tensor or
Maxwell bivector) is a
mathematical object that
describes the
electromagnetic field in spacetime...
- number) part and a
bivector part. (A
scalar is a
quantity with no orientation, a
vector is a
quantity oriented like a line, and a
bivector is a
quantity oriented...
-
geometric algebra, with the
planes of
rotations ****ociated with
simple bivectors in the algebra.
Planes of
rotation are not used much in two and three...
- or
wedge product – a
binary operation on two
vectors that
results in a
bivector. In
Euclidean 3-space, the
wedge product a ∧ b {\displaystyle \mathbf {a}...
- 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...
-
graded multivectors:
scalars are
grade 0,
usual vectors are
grade 1,
bivectors are
grade 2 and the
highest grade (3 in the 3D case) is traditionally...
