# Tag Info

The trick is trying to find out why that matrix has real eigenvalues in the first place. Usually it is because a suitable set of conjugations turns it into a symmetric matrix, and then you can reduce to a symmetric computation. Multiplying and dividing by $(AC)^{-1}$ you can rewrite $$D_1 = C^{-1}BAC (C^{-1}BAC+I)^{-1},$$ so your computation is equivalent ...