Fixing two eigenvalues by a minimal perturbation

DOI10.1016/j.laa.2005.04.004zbMath1089.15017OpenAlexW1973298267MaRDI QIDQ2566762

Ross A. Lippert

Publication date: 28 September 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.04.004

zbMATH Keywords

matrix perturbationeigenvalue perturbationEckart-Young theoremsingular value perturbation

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (12)

Nearest linearly structured polynomial matrix with some prescribed distinct eigenvalues ⋮ On the distance from a matrix polynomial to matrix polynomials with some prescribed eigenvalues ⋮ Perturbation analysis on matrix pencils for two specified eigenpairs of a semisimple eigenvalue with multiplicity two ⋮ Nearest matrix with prescribed eigenvalues and its applications ⋮ On the distance from a matrix polynomial to matrix polynomials with k prescribed distinct eigenvalues ⋮ Nearest matrix with a prescribed eigenvalue of bounded multiplicities ⋮ Perforated strict pseudospectra of Demmel's matrices ⋮ Fixing multiple eigenvalues by a minimal perturbation ⋮ On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue ⋮ Nearest southeast submatrix that makes multiple a prescribed eigenvalue. ⋮ Unnamed Item ⋮ Computational aspect to the nearest matrix with two prescribed eigenvalues

Uses Software

• JDQR
• JDQZ

Cites Work

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• Numerical computation of an analytic singular value decomposition of a matrix valued function
• Perturbation theory for linear operators.
• A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
• A formula for computation of the real stability radius
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
• Inverse Eigenvalue Problems
• On perturbations of matrix pencils with real spectra. II

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