3 problems

Let $\mathbb K\langle\underline{x}\rangle$ denote the free noncommutative polynomial algebra, let $\mathfrak r=(p_{ij})\in\mathbb K\langle\underline{x}\rangle^{L\times L}$ have non…

Matrix inverse realization conjecture. Each entry of $\mathfrak A^{-1}$ is a noncommutative rational expression in the entries of $\mathfrak A$: there exist noncommutative rational…

A noncommutative Givone–Roesser system has state-space decomposition $\mathbb{K}^m=\mathbb{K}^{m_1}\oplus\cdots\oplus\mathbb{K}^{m_d}$ and transfer function … where $A$ is a…