Let $C$ be a fixed real $n\times n$ matrix, $X$ be an arbitrary real $n\times n$ matrix. Find the minimum value of:
When $n=1$ it's clear that the minimum value equal $|C|$, however it seems like with $n\ge2$ the minimum value is exactly zero, but I don't know how to prove it.
Also I have found out that this is relating to the minimum of $\det(I+Q^2)$ with $I$ is identity and $Q$ is arbitrary real matrix. If you can evaluate either:
it would be appreciated!