Definition of Antilinear. Meaning of Antilinear. Synonyms of Antilinear

- {\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...
- {\displaystyle \mathbb {C} } is taken to be the standard topology) and antilinear, if one considers C {\displaystyle \mathbb {C} } as a complex vector space...
- x\in V.} A linear isometry (resp. an antilinear isometry) is an isometry that is also a linear map (resp. an antilinear map). For inner product spaces, the...
- 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...
- linearity of the other argument by complex conjugation (referred to as being antilinear in the other argument). This case arises naturally in mathematical physics...
- 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...
- 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...