6 problems

Robust eigenvectors conjecture. The robust eigenvectors of a regular simplex tensor are precisely the vectors in the frame.

Let $\mathbf{w}_1,\ldots,\mathbf{w}_{n+1}\in\mathbb{R}^n$ be the vectors of a regular simplex frame, and let … be the associated symmetric tensor of order $m$ and dimension $n$, wh…

Let $\mathcal{T}$ be an equiangular tight frame decomposable tensor, meaning a symmetric tensor admitting a decomposition into powers of vectors from an equiangular tight frame. Th…

Let $\mathcal{T}$ be a regular simplex tensor generated by a regular simplex frame. An eigenvector is a nonzero vector $\mathbf{x}$ satisfying … for some scalar $\lambda$, with eig…

Algebraic-multiplicity conjecture. If the algebraic multiplicity of an eigenvalue $\lambda\in\sigma(\mathcal A)$ is one, then a corresponding eigenvector is nondegenerate. This is…

Generic count conjecture. It is conjectured that $\mathcal N(n,k)$ is equal to $\frac{(k-1)^n-1}{k-2}$. The exact value of $\mathcal N(n,k)$ is otherwise stated to be unknown, whil…