I wonder if I can find for any matrix $B\in \mathbb{R}^{n\times n}$ a regular matrix $A\in \mathbb{R}^{n\times n}$ that minimises
$$ || A^{-1} B A - Id ||_F $$ where $||.||_F$ denotes the frobenius norm. Is this maybe equivalent to a convex minimization problem?
