Conjugate linear

In mathematics, a mapping ${\displaystyle f:V\to W}$ from a complex vector space to another is said to be antilinear (or conjugate-linear) if

for all ${\displaystyle a,\,b\,\in \mathbb {C} }$ and all ${\displaystyle x,\,y\,\in V}$, where ${\displaystyle {\bar {a}}}$ and ${\displaystyle {\bar {b}}}$ are the complex conjugates of ${\displaystyle a}$ and ${\displaystyle b}$ respectively. The composition of two antilinear maps is complex-linear. The class of semilinear maps generalizes the class of antilinear maps.

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