Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices -- application of perturbation theory for simple invariant subspaces

DOI10.1016/j.laa.2006.06.015zbMath1151.15306OpenAlexW2062752239MaRDI QIDQ865437

Xiezhang Li, Yi-Min Wei, Fanbin Bu, Fuzhen Zhang

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.06.015

zbMATH Keywords

eigenvaluesgroup inverseseparation functionrelative perturbation bounddiagonalizable and singular matrixsimple invariant subspaces

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items (22)

Acute perturbation of the group inverse ⋮ Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra ⋮ A note on the representations for the Drazin inverse of \(2 \times 2\) block matrices ⋮ A sharp version of Bauer-Fike's theorem ⋮ On additive properties of the Drazin inverse of block matrices and representations ⋮ Perturbation bounds for the group inverse and its oblique projection ⋮ Some block matrices with signed Drazin inverses ⋮ A note on the representation for the Drazin inverse of \(2 \times 2\) block matrices ⋮ Comment on ``condition number of Drazin inverse and their condition numbers of singular linear systems ⋮ Acute perturbation of Drazin inverse and oblique projectors ⋮ Continuity properties of the \(\{1\}\)-inverse and perturbation bounds for the Drazin inverse ⋮ Representations for generalized Drazin inverse of operator matrices over a Banach space ⋮ Further results on the perturbation estimations for the Drazin inverse ⋮ Comment on ``Condition number of \(W\)-weighted Drazin inverse and their condition numbers of singular linear systems ⋮ Some results on the generalized Drazin inverse of operator matrices ⋮ Representations for the Drazin inverse of the sum \(P+Q+R+S\) and its applications ⋮ On the eigenvalues of a specially updated complex matrix ⋮ Generalized Drazin inverses of anti-triangular block matrices ⋮ Quotient convergence and multi-splitting methods for solving singular linear equations ⋮ A note on the Drazin inverse of an anti-triangular matrix ⋮ The Drazin inverse of the sum of four matrices and its applications ⋮ A note on additive results for the Drazin inverse

Cites Work

• Unnamed Item
• Norms and exclusion theorems
• On the perturbation of the group inverse and oblique projection
• Generalized inverses. Theory and applications.
• A perturbation bound for the eigenvalues of a singular diagonalizable matrix
• Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
• Error Bounds for Approximate Invariant Subspaces of Closed Linear Operators

This page was built for publication: Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices -- application of perturbation theory for simple invariant subspaces