6 problems

Let $E,F:\mathcal I\rightarrow\mathbb{R}^{m\times m}$ be sufficiently smooth, and let $\{E,F\}$ be a regular pair with index $\mu\geq 2$. Write $r$ for the dimension of the differe…

Let $\mathfrak{g} = \operatorname{sl}(n) \ltimes \left(\mathbb{C}^n\right)^k$ be the semi-direct sum given by the standard representation, with $k<n$ and … Assume $1<r<k-1$. Almost…

Generic double multiplicity conjecture. There exists a generic set $\Omega\subseteq\mathbb R^{n,k}$ such that, for every $U\in\Omega$ and every $\tau\in\mathbb R\setminus\{0\}$, th…

Let the Riemannian optimization method proposed in this paper and the Das–Bora algorithm be applied to matrix pencils of increasing size, and compare their running times and the qu…

Let $P(\lambda)=\lambda(J_1+R_1)+(J_2+R_2)$ be a posH pencil, and let $\lambda J_1+J_2$ be its underlying skew-Hermitian pencil. Right-half-plane eigenvalue localization conjecture…

Let $T(x)=M_0+xM_1$, where $M_0$ and $M_1$ are the displayed $n\times n$ matrices, $n\geq 2$, with $c_1,c_2,\dots,c_{n+1}\in\mathbb C$ all non-zero, and $x$ an indeterminate over…