Corpus ID: 14690583

Sylvester's Influence on Applied Mathematics

@inproceedings{Higham2014SylvestersIO,
  title={Sylvester's Influence on Applied Mathematics},
  author={Nicholas John Higham},
  year={2014}
}
James Joseph Sylvester coined the term ``matrix'' and contributed much to the early development of matrix theory. To mark the 200th anniversary of his birth I show how Sylvester's work on matrices continues to influence applied mathematics today. 

Figures from this paper

Indistinguishable quantum walks on graphs relative to a bipartite quantum walker
A distinguishability operator is defined for the continuous-time quantum walk (CTQW) of a bipartite quantum walker on two simply connected graphs, $W_{G_i,G_j} = U_{G_i}\left(t\right) \otimesExpand

References

SHOWING 1-10 OF 56 REFERENCES
Cayley, Sylvester, and Early Matrix Theory
2008 marks the 150th anniversary of “A Memoir on the Theory of Matrices” by Arthur Cayley (1821–1895) [3]—the first paper on matrix algebra. Prior to this paper the theory of determinants was wellExpand
On the history of the kronecker product
History reveals that what is today called the Kronecker product should be called the Zehfuss product.
James Joseph Sylvester, F.R.S. (1814–1897)
  • I. James
  • Sociology
  • Notes and Records of the Royal Society of London
  • 1997
Among British mathematicians of the Victorian age there may be others who are comparable with Sylvester in terms of scientific achievement, but surely none whose life story makes such fascinatingExpand
Weierstrass and the theory of matrices
The following essay is the third in a series devoted to the history of the theory of matrices.1 In [1975 a] I related Cauchy's important memoir on the characteristic roots of a real quadratic form toExpand
An Improved Schur-Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives
  • N. Higham, L. Lin
  • Computer Science, Mathematics
  • SIAM J. Matrix Anal. Appl.
  • 2013
TLDR
Numerical experiments show the new algorithms to be superior in accuracy to, and often faster than, the original Schur--Pade algorithm for computing matrix powers and more accurate than several alternative methods for computing the Frechet derivative. Expand
James Joseph Sylvester: jewish mathematician in a victorian world
The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century Mathematics
.-1. A Berlin Education.- 2. Professor at the Zurich Polytechnic.- 3. Berlin Professor.-4. The Paradigm.-5. Further Development of the Paradigm.-6. The Problem of Pfaff.-7. The Cayley-Hermite ProblemExpand
Applied Numerical Linear Algebra
TLDR
The symmetric Eigenproblem and singular value decomposition and the Iterative methods for linear systems Bibliography Index. Expand
The Quadratic Eigenvalue Problem
We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both theExpand
Modifying the inertia of matrices arising in optimization
Applications in constrained optimization (and other areas) produce symmetric matrices with a natural block 2 × 2 structure. An optimality condition leads to the problem of perturbing the (1,1) blockExpand
...
1
2
3
4
5
...