2 problems

Let $\mathcal{N}(\mathbb{C}^n)$ denote the set of nilpotent operators on $\mathbb{C}^n$, and let $\delta_n$ be the distance from the set of non-zero projections in…

Let $\mathbb{M}_n(\mathbb{C})$ be the algebra of $n\times n$ complex matrices, let $\mathcal{N}(\mathbb{C}^n)$ be the set of nilpotent operators, and let $\nu_{r,n}$ denote the dis…