4 problems

Let $V$ be a finite-dimensional vector space over $\mathbb K$ of positive dimension, and let $A,A^*,A^\varepsilon:V\to V$ be linear transformations. A Leonard pair is a pair of tra…

Xin–Zhang's determinant conjecture. The determinant of $C$ is

Let $N$ be a positive integer and let $T^-$ and $T^+$ be the $(N-1)\times(N-1)$ tridiagonal matrices with … for $j=1,\ldots,N-1$, and $T^\pm_{j,j+1}=T^\pm_{j+1,j}=1$. Assume $a>0$.…

Let $A\in\mathbb{R}^{n\times n}$ be a nonsingular matrix whose inverse has only nonzero elements in the lower triangle. Let $X$ be the inverse computed numerically by algorithm (KW…