Eigenconfigurations of Tensors

TL;DR

This paper explores the fixed points of tensors and symmetric tensors, extending the concept of eigenvalues from matrices to higher-order tensor structures in projective spaces.

Contribution

It introduces the study of eigenconfigurations of tensors, generalizing matrix eigenvalues to tensor settings and analyzing their fixed point configurations.

Findings

Characterization of fixed points of tensor maps

Extension of eigenvalue concepts to tensors

Analysis of eigenconfigurations in projective spaces

Abstract

Square matrices represent linear self-maps of vector spaces, and their eigenpoints are the fixed points of the induced map on projective space. Likewise, polynomial self-maps of a projective space are represented by tensors. We study the configuration of fixed points of a tensor or symmetric tensor.