On the Early History of the Singular Value Decomposition

@article{Stewart1993OnTE,
  title={On the Early History of the Singular Value Decomposition},
  author={G. W. Stewart},
  journal={SIAM Rev.},
  year={1993},
  volume={35},
  pages={551-566}
}
  • G. Stewart
  • Published 1 December 1993
  • Mathematics
  • SIAM Rev.
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. 
A variational approach of the rank function
In the same spirit as the one of the paper (Hiriart-Urruty and Malick in J. Optim. Theory Appl. 153(3):551–577, 2012) on positive semidefinite matrices, we survey several useful properties of the
Eigenvalue computation in the 20 th century Gene
TLDR
The main developments of this century, especially as they relate to one another, are sketched to give an impression of the state of the art at the turn of the authors' century.
Eigenvalue computation in the 20th century
Eigenvalue Computation in the 20 th
TLDR
The intention of this contribution is to sketch the main developments of this century, especially as they relate to one another, and to give an impression of the state of the art at the turn of the century.
A geometric perspective on the Singular Value Decomposition
This is an introductory survey, from a geometric perspec- tive, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view
Singular Values of Riemann Curvature Tensor
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular
Visual Differential Geometry and Beltrami’s Hyperbolic Plane
Historical wrongs are hard to right. In 1868 Eugenio Beltrami (Fig. 4.1) set the previously abstract hyperbolic geometry of Lobachevsky and Bolyai upon a firm and intuitive foundation by interpreting
A brief review on Singular Value Inequalities
Singular values are defined as the square root of the eigenvalues of a Hermitian, positive semidefinite matrix S * S for some square matrix S with the entries from the field of complex numbers, which
Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century
The most obvious points of contact between linear and matrix algebra and statistics are in the area of multivariate analysis. We review the way that, as both developed during the last century, the
...
...

References

SHOWING 1-10 OF 67 REFERENCES
The bidiagonal singular value decomposition and Hamiltonian mechanics: LAPACK working note No. 11
We consider computing the singular value decomposition of a bidiagonal matrix B. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric
Accurate Singular Values of Bidiagonal Matrices
TLDR
A new algorithm that computes all the sinusoid values of a bidiagonal matrix is presented, which is the final phase of the standard algorithm for the singular value decomposition of a general matrix.
On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
This paper surveys perturbation theory for the pseudo–inverse (Moore–Penrose generalized inverse), for the orthogonal projection onto the column space of a matrix, and for the linear least squares ...
Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation.
  • H. Weyl
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1949
an extension (T, y6) of Q such that T contains E as local subgroup and {1 E = q| E. We call the pair (Y, X) elementary with respect to Q if every extension of X is extensible over Q from Y. We can
Handbook for Automatic Computation. Vol II, Linear Algebra
TLDR
Haida gwaii tourism guide, Handbook of raman spectroscopy, and the Jordan form, Kronecker's form for matrix pencils, and various condition in the Handbook.
Topics in Matrix Analysis
1. The field of values 2. Stable matrices and inertia 3. Singular value inequalities 4. Matrix equations and Kronecker products 5. Hadamard products 6. Matrices and functions.
Matrix Perturbation Theory
TLDR
X is the vector space which acts in the n-dimensional (complex) vector space R.1.1 and is related to Varepsilon by the following inequality.
...
...