On the Early History of the Singular Value Decomposition

1993/12/01 by G. W. Stewart · 5 citations
Mathematics · Arts and Humanities · Medicine · #History and Theory of Mathematics #Philosophy and History of Science #Singular value decomposition #Value (mathematics) #Mathematics #Decomposition #Philosophy #Algebra over a field #Calculus (dental) #Mathematical economics #Pure mathematics #Statistics #Algorithm #Medicine

paper · doi:10.1137/1035134

openalex publication_date 1993/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper surveys the contributions of five mathematicians—Eugenio Beltrami (1835–1899), Camille Jordan (1838–1921), James Joseph Sylvester (1814–1897), Erhard Schmidt (1876–1959), and Hermann Weyl (1885–1955)—who were responsible for establishing the existence of the singular value decomposition and developing its theory.

Citations

• The Rotation of Eigenvectors by a Perturbation. III
• A generalized inverse for matrices
• The Approximation of One Matrix by Another of Lower Rank
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• A Generalized Solution of the Orthogonal Procrustes Problem
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• Analysis of a complex of statistical variables into principal components.
• Accurate Singular Values of Bidiagonal Matrices
• Singular value decomposition and least squares solutions
• Zur Theorie der linearen und nichtlinearen Integralgleichungen

Cited by

• Tensor optimization for optical-interferometric imaging
• Continuous analogues of matrix factorizations
• On Universal Features for High-Dimensional Learning and Inference
• Eigenvalue computation in the 20th century
• Singular value decomposition [wikipedia]