- mathematics, a
linear form (also
known as a
linear functional, a one-form, or a
covector) is a
linear map from a
vector space to its
field of
scalars (often, the...
-
vectors are
often just
called vectors and
covariant vectors are
called covectors or dual vectors. The
terms covariant and
contravariant were introduced...
- of a
covector field along a
vector field v is
again a
covector field. Once the
covariant derivative is
defined for
fields of
vectors and
covectors it can...
-
components (not the i {\displaystyle i} th
covector v {\displaystyle v} ), w {\displaystyle w} is the
covector and w i {\displaystyle w_{i}} are its components...
- In
differential geometry, a one-form (or
covector field) on a
differentiable manifold is a
differential form of
degree one, that is, a
smooth section of...
- ) ∗ {\displaystyle (\mathbb {R} ^{n})^{*}}
denotes the dual
space of
covectors,
linear functions v ∗ : R n → R {\displaystyle v^{*}:\mathbb {R} ^{n}\to...
-
length of (or
angle between)
covector fields; that is,
fields of
linear functionals. To see this,
suppose that α is a
covector field. To wit, for each point...
- (with n-dimensional indices,
summation implied). A
covariant vector, or
covector, is a
system of
functions v k {\displaystyle v_{k}} that
transforms under...
-
applied to
vector fields and
covector fields by
applying them to each point. Hence, if X is a
vector field and ω is a
covector field, X ♭ = g ( X , ⋅ ) {\displaystyle...
- The
covector mapping principle is a
special case of Riesz'
representation theorem,
which is a
fundamental theorem in
functional analysis. The name was...
