We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of giving a description of the correctable erasure patterns in a maximally recoverable tensor code with the problem of describing bipartite rigid graphs or low-rank completable matrix patterns. Additionally, we relate dependencies among symmetric products of generic vectors to graph rigidity and symmetric matrix completion. With an eye toward applications to computer science, we study the dependency of these matroids on the characteristic by giving new combinatorial descriptions in several cases, including the first description of the correctable patterns in an (m, n, a=2, b=2) maximally recoverable tensor code.

翻译：本文建立了刚性理论中研究的问题与张量积、对称积等线性代数构造产生的拟阵之间的联系。该对应关系的特例将最大可恢复张量码中可纠擦除模式的描述问题，与描述二分刚性图或低秩可补矩阵模式的问题等同起来。此外，我们还将泛型向量对称积之间的依赖关系与图刚性及对称矩阵补全相关联。着眼于计算机科学中的应用，我们通过给出若干新情况的组合描述来研究这些拟阵对特征的依赖，包括首次给出（m, n, a=2, b=2）最大可恢复张量码中可纠模式的描述。