Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver. Consequently, we are able to define and compute principal components with respect to quiver representations. These principal components are solutions to constrained optimisation problems defined over the space of sections and are eigenvectors of an associated matrix pencil.

中文翻译：

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沿着 Quiver 表示的主成分

箭袋表示自然地出现在数学的许多领域。在这里，我们描述了一种算法，用于计算有限箭袋的任何有限维表示的部分的向量空间，或向量到顶点的兼容分配。因此，我们能够定义和计算关于 quiver 表示的主成分。这些主成分是在截面空间上定义的约束优化问题的解决方案，并且是相关矩阵铅笔的特征向量。