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In mathematics, a function between two complex vector spaces is said to be antilinear or conjugate-linear if hold for all vectors and every complex number where denotes the complex conjugate of Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate homogeneous. If the vector spaces are real then antilinearity is the same as linearity.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Relation100031921 yago:WikicatFunctionsAndMappings
rdfs:label	Konjuglineara bildigo (eo) Antilinear map (en) Trasformazione antilineare (it) Przekształcenie antyliniowe (pl) 反线性映射 (zh)
rdfs:comment	En matematiko, f : V → W de al alia estas konjuglineara aŭ konjugita-lineara aŭ kontraŭlineara se f(ax+by) = a* f(x) + b* f(y) por ĉiuj a, b en C kaj ĉiuj x, y en V, kie z* estas la kompleksa konjugito de z. La komponaĵo de du konjuglinearaj mapoj estas . Konjuglineara mapo povas esti ekvivalente priskribita en terminoj de la lineara bildigo al la W*. (eo) Przekształcenie antyliniowe (przekształcenie półliniowe) – rodzaj przekształcenia między zespolonymi przestrzeniami liniowymi. (pl) 在数学中，从一个复数向量空间到另一个复数向量空间的映射 f : V → W 被称为是反线性的（或共轭线性或半线性的）如果对于所有 C 中 a, b 和 V 中所有 x, y。两个反线性映射的复合是线性的。反线性映射可以等价的描述为到的线性映射。 (zh) In mathematics, a function between two complex vector spaces is said to be antilinear or conjugate-linear if hold for all vectors and every complex number where denotes the complex conjugate of Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate homogeneous. If the vector spaces are real then antilinearity is the same as linearity. (en) In matematica si dice trasformazione antilineare, applicazione antilineare, funzione antilineare, mappa antilineare o operatore antilineare una trasformazione da uno spazio vettoriale sui complessi in un secondo spazio dello stesso genere se: dove è il complesso coniugato di . Queste entità talvolta sono chiamate trasformazione coniugatolineare e trasformazione semilineare. Se insieme alla precedente si considera una seconda trasformazione antilineare del genere che conduce ad un terzo spazio vettoriale sui complessi , la composizione di con è una trasformazione lineare complessa . (it)
dcterms:subject	Functions and mappings Linear algebra
Wikipage page ID	293432 (xsd:integer)
Wikipage revision ID	1095448355 (xsd:integer)
Link from a Wikipage to another Wikipage	Homogeneous Complex conjugate vector space Complex number Continuous dual space Mathematics Function (mathematics) Linear operator Complex conjugate Composition of relations T-symmetry Topological vector space Dual norm Linear map Additive map Functions and mappings Linear algebra Normed space Parallelogram law Hilbert space Isometry Homeomorphism Polarization identity Real vector space Inner product space Semilinear map Bijective map Conjugate homogeneity Conjugate homogeneous Complex vector space Anti-dual space Homogeneous map dbr:Spinor_calculus
sameAs	Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map Antilinear map
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Em dbt:Reflist dbt:Sfn dbt:Short_description dbt:Isbn dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Linear-algebra-stub
has abstract	In mathematics, a function between two complex vector spaces is said to be antilinear or conjugate-linear if hold for all vectors and every complex number where denotes the complex conjugate of Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate homogeneous. If the vector spaces are real then antilinearity is the same as linearity. Antilinear maps occur in quantum mechanics in the study of time reversal and in , where it is customary to replace the bars over the basis vectors and the components of geometric objects by dots put above the indices. Scalar-valued antilinear maps often arise when dealing with complex inner products and Hilbert spaces. (en) En matematiko, f : V → W de al alia estas konjuglineara aŭ konjugita-lineara aŭ kontraŭlineara se f(ax+by) = a* f(x) + b* f(y) por ĉiuj a, b en C kaj ĉiuj x, y en V, kie z* estas la kompleksa konjugito de z. La komponaĵo de du konjuglinearaj mapoj estas . Konjuglineara mapo povas esti ekvivalente priskribita en terminoj de la lineara bildigo al la W*. (eo) In matematica si dice trasformazione antilineare, applicazione antilineare, funzione antilineare, mappa antilineare o operatore antilineare una trasformazione da uno spazio vettoriale sui complessi in un secondo spazio dello stesso genere se: dove è il complesso coniugato di . Queste entità talvolta sono chiamate trasformazione coniugatolineare e trasformazione semilineare. Se insieme alla precedente si considera una seconda trasformazione antilineare del genere che conduce ad un terzo spazio vettoriale sui complessi , la composizione di con è una trasformazione lineare complessa . Una trasformazione antilineare è equivalente ad una trasformazione lineare del genere che conduce allo . Per un operatore antilineare la definizione di aggiunta è diversa da quella usuale: in cui l'operatore risulta correttamente antilineare in e . (it) Przekształcenie antyliniowe (przekształcenie półliniowe) – rodzaj przekształcenia między zespolonymi przestrzeniami liniowymi. (pl) 在数学中，从一个复数向量空间到另一个复数向量空间的映射 f : V → W 被称为是反线性的（或共轭线性或半线性的）如果对于所有 C 中 a, b 和 V 中所有 x, y。两个反线性映射的复合是线性的。反线性映射可以等价的描述为到的线性映射。 (zh)
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page length (characters) of wiki page	10532 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Antilinear_map
is Link from a Wikipage to another Wikipage of	Bra–ket notation Antiunitary operator Homogeneous function Riesz representation theorem Fundamental theorem of Hilbert spaces Corepresentations of unitary and antiunitary groups Antilinear Antilinear mapping Linear form Complex conjugate Complex conjugate of a vector space Complex torus Matrix consimilarity Banach space Wigner's theorem Hermitian adjoint Hilbert space Real structure Polarization identity Inner product space Semilinear map Semilinear Sesquilinear form

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