Taking $\Theta=0$ gives $\lVert\Sigma\Theta-I\rVert_{\max}=1$, so every matrix is $1$-invertible. The smallest admissible value is
$$
\inf_\Theta\lVert\Sigma\Theta-I\rVert_{\max}.
$$
The map inside the norm is affine in $\Theta$, and a norm composed with an affine map is a <convex function>. The space of matrices is a convex feasible set, so this is a <convex optimization> problem.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 205 / 6 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-205/6/a/solution