Eigenvectors of tensors - A primer

TL;DR

This paper provides an accessible introduction to the theory of tensor eigenvectors, covering fundamental concepts, results, and applications to help practitioners understand this mathematical area.

Contribution

It offers a comprehensive primer on tensor eigenvectors, summarizing key ideas, methods, and applications for practitioners new to the field.

Findings

Overview of tensor eigenvector theory

Summary of key concepts and techniques

Discussion of applications in various fields

Abstract

We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their discussion. The intent is to give practitioners an overview of fundamental notions, results and techniques.