- {\displaystyle f:V\to W}
between two
complex vector spaces is said to be
antilinear or conjugate-linear if f ( x + y ) = f ( x ) + f ( y ) (additivity) ...
- bounded; the same is true of
antilinear maps. The
inverse of any
antilinear (resp. linear)
bijection is
again an
antilinear (resp. linear) bijection. The...
-
imaginary part of a
complex inner product depends on
which argument is
antilinear.
Antilinear in
first argument The
polarization identities for the
inner product...
-
complex vector space V with an
invariant quaternionic structure, i.e., an
antilinear equivariant map j : V → V {\displaystyle j\colon V\to V}
which satisfies...
-
complex vector spaces, a
function f : V → W {\displaystyle f:V\to W} is
antilinear if f ( v + w ) = f ( v ) + f ( w ) and f ( α v ) = α ¯ f ( v ) {\displaystyle...
- {\displaystyle \mathbb {C} } is
taken to be the
standard topology) and
antilinear, if one
considers C {\displaystyle \mathbb {C} } as a
complex vector space...
-
linearity of the
other argument by
complex conjugation (referred to as
being antilinear in the
other argument). This case
arises naturally in
mathematical physics...
- In mathematics, an
antiunitary transformation is a
bijective antilinear map U : H 1 → H 2 {\displaystyle U:H_{1}\to H_{2}\,}
between two
complex Hilbert...
- on a
complex vector space V with an
invariant real structure, i.e., an
antilinear equivariant map j : V → V {\displaystyle j\colon V\to V}
which satisfies...
-
function f : H → C {\displaystyle \mathbb {C} } is
called semilinear or
antilinear if for all x, y ∈ H and all
scalars c , Additive: f (x + y) = f (x) +...
