English

A Geometric Perspective on the Singular Value Decomposition

Algebraic Geometry 2015-03-25 v1

Abstract

This is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of a tensor as the space spanned by singular vector tuples and we study some of its basic properties.

Keywords

Cite

@article{arxiv.1503.07054,
  title  = {A Geometric Perspective on the Singular Value Decomposition},
  author = {Giorgio Ottaviani and Raffaella Paoletti},
  journal= {arXiv preprint arXiv:1503.07054},
  year   = {2015}
}

Comments

20 pages, 2 figures. Keywords: Singular Value Decomposition, Tensor To be published in Rend. Istit. Mat. Univ. Trieste

R2 v1 2026-06-22T09:00:46.862Z