Intuitive Interpretations of SVD Vectors

Abstract

Summary The SVD is currently becoming an increasingly important central pillar in linear algebra. A voice as authoritative and influential as Gil Strang’s remarked that although a few years ago the SVD was not even part of an introductory linear algebra course, “now it has to be.” To balance the already firmly established theoretical basis, we survey several intuitive conceptualizations for singular vectors and values, expand on them, and provide some original contributions.