A singular m-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it d-stable?

@article{Bierkens2014ASM,
  title={A singular m-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it d-stable?},
  author={Joris Bierkens and Andr{\'e} C. M. Ran},
  journal={Linear Algebra and its Applications},
  year={2014},
  volume={457},
  pages={191-208}
}
  • J. Bierkens, A. Ran
  • Published 30 November 2013
  • Mathematics
  • Linear Algebra and its Applications
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References

SHOWING 1-10 OF 19 REFERENCES
Jordan forms of real and complex matrices under rank one perturbations
New perturbation results for the behavior of eigenvalues and Jordan forms of real and complex matrices under generic rank one perturbations are discussed. Several results that are available in the
Eigenvalues of rank-one updated matrices with some applications
Nonnegative Matrices in the Mathematical Sciences
1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative
Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations
We study the perturbation theory of structured matrices under structured rank one perturbations, with emphasis on matrices that are unitary, orthogonal, or symplectic with respect to an indefinite
Eigenvalue perturbation theory of structured matrices under generic structured rank one perturbations : Symplectic , orthogonal , and unitary matrices ∗
We study the perturbation theory of structured matrices under structured rank one perturbations, with emphasis on matrices that are unitary, orthogonal, or symplectic with respect to an indefinite
On the Change in the Spectral Properties of a Matrix under Perturbations of Sufficiently Low Rank
We show that the r largest Jordan blocks disappear and all other blocks remain the same in the part of the Jordan form corresponding to a given eigenvalue λ under a generic rank r perturbation.
...
...