Realification determinant identity
= Realification determinant identity
{title2=$\det_{\mathbb R}\mathcal R(A)=|\det_{\mathbb C}A|^2$}
The <realification of a complex matrix> has real determinant $|\det_{\mathbb C}A|^2$. Indeed the invertible complex coordinate change $(x,y)\mapsto(x+iy,x-iy)$ conjugates its complexified block matrix to $\operatorname{diag}(A,\overline A)$. Taking determinants gives the identity, including singular matrices.