2 problems

Let $X$ be either ${\mathcal{M}}_n({\mathbb{F}})$ or ${\mathcal{H}}_n({\mathbb{F}})$, let $\|\cdot\|$ be an admissible norm on $X$, and write $k=\dim X$. For a placement $p\in X^V$…

Let $r,d \in \mathbb{N}$, let $\mathcal{I}_r(\mathbb{K}^d)$ be the ambient class of $r$-tuples under consideration, and let $\Omega_r^n$ denote the words of length $n$. For…