Complex-linear map
= Complex-linear map
{title2=$A(iv)=iA(v)$}
A real-linear map between <complex vector spaces> that commutes with multiplication by $i$. On $\mathbb C$, its real matrix is $\begin{pmatrix}a&-b\\b&a\end{pmatrix}$, representing multiplication by $a+ib$. On $\mathbb C$, such a map with real <determinant> one is a rotation. In higher complex dimension, determinant one does not force the map to be a <unitary operator>.