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：我们建立了刚性理论中研究的问题与张量积和对称积等线性代数构造产生的拟阵之间的联系。这种对应关系的一个特例，将描述最大可恢复张量码中可纠正擦除模式的问题，与描述二分刚性图或低秩可补全矩阵模式的问题相统一。此外，我们将一般向量对称积之间的依赖关系与图刚性及对称矩阵补全联系起来。着眼于计算机科学的应用，我们通过给出若干情形下的新组合描述（包括首次描述(m, n, a=2, b=2)最大可恢复张量码中的可纠正模式），研究了这些拟阵对域特征的依赖性。