Principal Components Along Quiver Representations
Principal Components Along Quiver Representations
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DOI：
10.1007/s10208-022-09563-x
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发表时间：
2021-04
影响因子：
3
通讯作者：
A. Seigal;H. Harrington;Vidit Nanda
中科院分区：
文献类型：
--
作者：
A. Seigal;H. Harrington;Vidit Nanda
箭图表示法在数学的许多领域中自然出现。在这里，我们描述了一个算法，用于计算部分的向量空间，或向量到顶点的兼容分配，任何有限维表示的有限向量。因此，我们能够定义和计算主成分相对于双线性表示。这些主成分是定义在截面空间上的约束优化问题的解决方案，并且是相关矩阵束的特征向量。
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.