This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop \emph{Linear Systems and Eigenvalue Problems}, which was organized at the Simons Institute for the Theory of Computing program on \emph{Complexity and Linear Algebra} in Fall 2025. The complexity and numerical solution of linear algebra problems %in matrix computations and related fields is a crosscutting area between theoretical computer science and numerical analysis. The value of the particular problem formulations here is that they were produced via discussions between researchers from both groups. The open questions are organized in five categories: iterative solvers for linear systems, eigenvalue computation, low-rank approximation, randomized sketching, and other areas including tensors, quantum systems, and matrix functions.

翻译：本文档呈现了矩阵计算领域（即线性代数问题的数值解法）中涌现的一系列开放性问题。这些问题是2025年秋季在"计算复杂性理论与线性代数"项目框架下，由西蒙斯理论计算研究所组织的"线性系统与特征值问题"研讨会工作组的成果。线性代数问题的计算复杂性与数值解法构成了理论计算机科学与数值分析之间的交叉领域。本文所提问题表述的特殊价值在于，它们源自两个研究群体学者间的深入讨论。开放性问题被划分为五个类别：线性系统的迭代求解器、特征值计算、低秩近似、随机草图技术，以及其他领域（包括张量、量子系统和矩阵函数）。