Definition of Antilinear. Meaning of Antilinear. Synonyms of Antilinear

Here you will find one or more explanations in English for the word Antilinear. Also in the bottom left of the page several parts of wikipedia pages related to the word Antilinear and, of course, Antilinear synonyms and on the right images related to the word Antilinear.

Definition of Antilinear

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Meaning of Antilinear from wikipedia

- {\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...