Rank one perturbations of \(H\)-positive real matrices

DOI10.1016/j.laa.2013.04.010zbMath1283.15102OpenAlexW2036232040MaRDI QIDQ2435366

André C. M. Ran, Jan H. Fourie, D. B. Janse van Rensburg, Gilbert J. Groenewald

Publication date: 19 February 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2013.04.010

zbMATH Keywords

eigenvalueJordan canonical formskew symmetric matrixrank one perturbation\(H\)-positive real matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03) Canonical forms, reductions, classification (15A21)

Related Items (7)

Low-rank perturbation of regular matrix pencils with symmetry structures ⋮ A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable? ⋮ Generic rank-one perturbations of structured regular matrix pencils ⋮ Simple forms and invariant subspaces of \(H\)-expansive matrices ⋮ An alternative canonical form for quaternionic \(H\)-unitary matrices ⋮ Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices ⋮ Unifying Matrix Stability Concepts with a View to Applications

Cites Work

• Eigenvalues of rank one perturbations of unstructured matrices
• Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations
• Inertia characteristics of self-adjoint matrix polynomials
• Typical changes in spectral properties under perturbation by an operator of rank one.
• Similarity vs unitary similarity and perturbation analysis of sign characteristics: complex and real indefinite inner products
• Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence
• Jordan forms of real and complex matrices under rank one perturbations
• Low Rank Perturbation of Jordan Structure
• A Remark on Perturbations of Compact Operators.

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