Nearest southeast submatrix that makes multiple a prescribed eigenvalue.

DOI10.1016/j.laa.2008.10.012zbMath1194.15024OpenAlexW2083230866MaRDI QIDQ999800

J. Martínez

Publication date: 10 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.012

zbMATH Keywords

controllableobservablemultiple eigenvaluenearest matrixderivatives of singular valuesWilkinson's problem

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Canonical structure (93B10) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (2)

Nearest matrix with a prescribed eigenvalue of bounded multiplicities ⋮ Unnamed Item

Cites Work

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• Sensitivity analysis of all eigenvalues of a symmetric matrix
• Geometric multiplicity margin for a submatrix
• Nearest matrix with two prescribed eigenvalues
• A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
• Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem
• A formula for computation of the real stability radius
• Singular values and invariant factors of matrix sums and products
• Fixing two eigenvalues by a minimal perturbation
• The Smallest Perturbation of a Submatrix which Lowers the Rank and Constrained Total Least Squares Problems
• Second-order directional derivatives of all eigenvalues of a symmetric matrix

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