  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.
