= Realification of a complex matrix
{title2=$\mathcal R(A)=\begin{pmatrix}\operatorname{Re}A&-\operatorname{Im}A\\\operatorname{Im}A&\operatorname{Re}A\end{pmatrix}$}
For $A=P+iQ$ with real matrices $P,Q$, the same <linear map> viewed over the reals has block matrix $\begin{pmatrix}P&-Q\\Q&P\end{pmatrix}$ 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>.
Back to article page
