nLab antilinear map

Definition

Given $V$ a complex vector space, a function $f \colon V \to V$ as antilinear or conjugate linear if

• it respects sums of vectors: for all $v_1, v_2$ in $V$ we have $f(v_1 + v_2) = f(v_1) + f(v_2)$

• it preserves multiplication by complex numbers up to complex conjugation $\overline{(-)}$: for all $c \in \mathbb{C}$ and $v \in c$ we have $f(c \cdot v) = \overline{c}\cdot f(v)$.

Related concepts

• real structure