Antilinear map
From Free net encyclopedia
In mathematics, a mapping f : V → W from a complex vector space to another is said to be antilinear (or conjugate-linear or semilinear) if
- <math>f(ax+by)=\bar{a}f(x)+\bar{b}f(y)</math>
for all a, b in C and all x, y in V. The composition of two antilinear maps is complex-linear.
An antilinear map <math>f:V\to W</math> may be equivalently described in terms of linear map <math>\bar f:V\to\bar W</math> to the complex conjugate vector space <math>\bar W</math>.
[edit]