2 problems

Let $n$ be a positive integer, let $\mathbb{M}_n$ be the algebra of $n\times n$ complex matrices, and let $P\in {\mathcal{P}}(\mathbb{M}_n)$ be a projection of rank $m$, where…

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…