Matrix Perturbation Theory

  title={Matrix Perturbation Theory},
  author={G. W. Stewart and Ji-guang Sun},
The Symmetric Eigenvalue and Singular-Value Problems
Eigenvalue problems form the second most important class of problems in numerical linear algebra.
Perturbations of simple eigenvectors¶of linear operators
Abstract:Residual bounds for perturbed simple eigenvectors of linear operators are derived.
Perturbation bound of singular linear systems
  • Yi-min Wei
  • Mathematics, Computer Science
    Appl. Math. Comput.
  • 1999
Perturbed spectra of defective matrices
This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A
Discrete Symplectic Eigenvalue Problems
In this chapter we investigate eigenvalue problems associated with symplectic system ( SDS), where the coefficient matrix depends on a spectral parameter.
Singular Values and Doubly Stochastic Matrices
The Hadamard square of any square matrix A is bounded above and below by some doubly stochastic matrices times the square of the largest and the smallest singular values of A.