The Euclidean distance degree of orthogonally invariant matrix varieties

DOI10.1007/s11856-017-1545-4zbMath1402.14073arXiv1601.07210OpenAlexW2963583989MaRDI QIDQ1678646

Dmitriy Drusvyatskiy, Hon-Leung Lee, Giorgio Ottaviani, Rekha R. Thomas

Publication date: 17 November 2017

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.07210

zbMATH Keywords

real algebraic varietytransfer principleEuclidean distance degreeinvariant matrix varieties

Mathematics Subject Classification ID

Quadratic programming (90C20) Real algebraic sets (14P05) Computational aspects of higher-dimensional varieties (14Q15)

Related Items (10)

Tensors with eigenvectors in a given subspace ⋮ A note on ED degrees of group-stable subvarieties in polar representations ⋮ The critical space for orthogonally invariant varieties ⋮ Exact solutions in low-rank approximation with zeros ⋮ Explicit Global Minimization of the Symmetrized Euclidean Distance by a Characterization of Real Matrices with Symmetric Square ⋮ The distance function from a real algebraic variety ⋮ On the geometry of the set of symmetric matrices with repeated eigenvalues ⋮ Asymptotics of degrees and ED degrees of Segre products ⋮ Spectral Operators of Matrices: Semismoothness and Characterizations of the Generalized Jacobian ⋮ Best rank-\(k\) approximations for tensors: generalizing Eckart-Young

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Euclidean distance degree of Fermat hypersurfaces
• Euclidean distance degrees of real algebraic groups
• Computational invariant theory. With two appendices by Vladimir L. Popov and an addendum by Nobert A. Campo and Vladimir L. Popov
• Elementary structure of real algebraic varieties
• All convex invariant functions of hermitian matrices
• On the differentiability of O(n) invariant functions of symmetric matrices
• The invariant theory of \(n\times n\) matrices
• The red book of varieties and schemes. Includes the Michigan lectures (1974) on ``Curves and their Jacobians.
• Theory of reconstruction from image motion
• Differentiability properties of isotropic functions
• The Chow form of the essential variety in computer vision
• A geometric perspective on the Singular Value Decomposition
• Orthogonal Invariance and Identifiability
• Counting Real Critical Points of the Distance to Orthogonally Invariant Matrix Sets
• An analog of the singular value decomposition for complex orthogonal equivalence
• Derivatives of Spectral Functions
• Continuity and Location of Zeros of Linear Combinations of Polynomials
• Approximating functions on stratified sets
• Algorithms in invariant theory
• The Euclidean distance degree of an algebraic variety

This page was built for publication: The Euclidean distance degree of orthogonally invariant matrix varieties