Relationship between the characteristic polynomial and the spectrum of a diagonalizable matrix and those of its low-rank update

DOI10.1080/03081087.2011.639372zbMath1253.65058OpenAlexW2037033118MaRDI QIDQ5200332

Gang Wu, Yi-Min Wei

Publication date: 5 November 2012

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

Full work available at URL: https://doi.org/10.1080/03081087.2011.639372

zbMATH Keywords

eigenproblemeigenvaluesspectrumcharacteristic polynomialsingular valuesdiagonalizable matrixlow-rank update

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (3)

The number of distinct eigenvalues of a regular pencil and of a square matrix after rank perturbation ⋮ Hypergraph analysis based on a compatible tensor product structure ⋮ Refined bounds on the number of distinct eigenvalues of a matrix after low-rank update

Cites Work

• On the eigenvalues of specially low-rank perturbed matrices
• The eigenvalue problem of a specially updated matrix
• Eigenvalues and Jordan canonical form of a successively rank-one updated complex matrix with applications to Google's PageRank problem
• On the eigenvalues of a specially updated complex matrix
• Google pageranking problem: The model and the analysis
• Eigenvalues of rank-one updated matrices with some applications
• Properties of the matrix \(A-XY^*\)
• Computing Characteristic Polynomials from Eigenvalues
• A General Setting for the Parametric Google Matrix
• Perturbation Bounds for Determinants and Characteristic Polynomials
• A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem
• Low rank update of singular values
• Some Modified Matrix Eigenvalue Problems

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