4 problems

Let $M$ be an $m \times n$ matrix with coefficients in $\mathscr{L}$ (or $\mathscr{L}_p$). Write … where $M_i \in M_{m \times n}(\mathbf{Q})$ and the $\lambda_i$ are elements of…

Let $R(n,k)$ be the matrix introduced in the paper, and let $R^{-1}(n,k)$ denote its inverse matrix. The fifth conjecture. (1) For fixed $k$ and any prime power $p^e$ with…

Polynomial-size fields conjecture. There exist triangular totally nonsingular matrices over finite fields of polynomial size.

Let $T_3^{\le 2}$ denote the specified binary matrix family, and let $\operatorname{sat}(n,F)$ be the minimum number of columns in an $n$-row $F$-saturated matrix. Set…