Antilinear

Antilinear

Als Semilinearform bezeichnet man in der linearen Algebra eine semilineare Abbildung aus einem Vektorraum in den diesem zugrundeliegenden Skalarkörper; relevant sind Semilinearformen lediglich über dem Körper C der komplexen Zahlen.

Eine Semilinearform f:V\longrightarrow K genügt den beiden folgenden Bedingungen, die ganz allgemein eine semilineare Abbildung kennzeichnen: für alle x, y aus V und alle λ aus K gilt:

  • (1) Superposition: f(x + y) = f(x) + f(y)
  • (2) komplex konjugierte Homogenität: f(\lambda x)=\overline{\lambda}f(x), wobei \overline{\lambda} das komplex Konjugierte von λ bezeichne.

Außer dem Begriff „semilinear“ finden sich in der Literatur auch die Begriffe „antilinear“ und „konjugiert linear“.

Siehe auch


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