Singular Vectors of Orthogonally Decomposable Tensors

TL;DR

This paper explores the spectral theory of orthogonally decomposable tensors, generalizing matrix SVD, by describing their singular vector tuples as a geometric variety.

Contribution

It provides a geometric description of singular vectors for orthogonally decomposable tensors, extending the spectral theory beyond matrices.

Findings

Singular vector tuples form a variety in a product of projective spaces.

The paper generalizes the concept of SVD to higher-order tensors.

Provides a theoretical framework for understanding tensor spectral properties.

Abstract

Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its singular vector tuples as a variety in a product of projective spaces.