# Perturbed spectra of defective matrices

@article{Konstantinov2003PerturbedSO,
title={Perturbed spectra of defective matrices},
author={Mihail Konstantinov and Volker Mehrmann and Petko Hr. Petkov},
journal={Journal of Applied Mathematics},
year={2003},
volume={2003},
pages={115-140}
}
• Published 5 March 2003
• Mathematics
• Journal of Applied Mathematics
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
4 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES
The algebraic eigenvalue problem
Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of
Computational methods for linear control systems
• Mathematics, Computer Science
• 1991
Numerical matrix computations linear control systems solution of state equations stability, controllability and observability computations pole assignment solution of matrix Riccati equations
The Theory of Matrices
Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices 2. Polar decomposition of a complex matrix 3. The normal form of
On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
• Mathematics
• 1997
Let A be a complex matrix with arbitrary Jordan structure and $\lambda$ an eigenvalue of A whose largest Jordan block has size n. We review previous results due to Lidskii [U.S.S. R. Comput. Math.
Algorithm 560: JNF, An Algorithm for Numerical Computation of the Jordan Normal Form of a Complex Matrix [F2]
• Computer Science
TOMS
• 1980
This work describes in detail how to use the For t ran subroutines and how to reach the results from a call and gives some comments on the code tha t might be of value when implementing the subRoutines on a part icular machine.
Matrix computations
The theory of matrices
• Mathematics
• 1969