Principal Components along Quiver Representations
Representation Theory
2021-11-25 v2
Abstract
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.
Cite
@article{arxiv.2104.10666,
title = {Principal Components along Quiver Representations},
author = {Anna Seigal and Heather A. Harrington and Vidit Nanda},
journal= {arXiv preprint arXiv:2104.10666},
year = {2021}
}
Comments
31 pages; v2: more examples, results added to section 5