 Realification of a complex matrix

For $A=P+iQ$ with real matrices $P,Q$, the same linear map viewed over the reals has block matrix $\left(\begin{array}{cc}P& -Q\\ Q& P\end{array}\right)$ in grouped real/imaginary coordinates. Interleaved coordinates merely permute the basis. Its complexification splits into the matrices $A$ and $\overline{A}$, giving the realification determinant identity.