Gershgorin's theorem for matrices of operators

DOI10.1016/S0024-3795(98)10219-7zbMath1018.47004MaRDI QIDQ1300843

Héctor N. Salas

Publication date: 11 September 2003

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

zbMATH Keywords

invariant subspacesnormal operatorsminimal Gershgorin setspartitioned matricesHilbert and Banach spacesRiesz projectionsGershgorin circle theorem

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Invariant subspaces of linear operators (47A15)

Related Items (14)

Block triangular preconditioning for stochastic Galerkin method ⋮ Schrödinger operators with complex sparse potentials ⋮ The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices ⋮ A new Gershgorin-type result for the localisation of the spectrum of matrices ⋮ The Ostrowski theorem for matrices of operators ⋮ Asymptotic behaviour of the non-real pair-eigenvalues of a two parameter eigenvalue problem ⋮ A time-based solution for the graph isomorphism problem ⋮ Spectral enclosures for some unbounded \(n\times n\) operator matrices ⋮ The generalized Brauer–Ostrowski theorem for matrices of operators ⋮ Spectral inclusion for unbounded diagonally dominant \(n\times n\) operator matrices ⋮ Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems ⋮ Singular value decomposition Geršgorin sets ⋮ The Kachurovskij spectrum of Lipschitz continuous nonlinear block operator matrices ⋮ Spectral enclosures for a class of block operator matrices

Cites Work

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• Eigenvalues for infinite matrices
• Note on circular disks containing the eigenvalues of a matrix
• Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem
• Spectral properties of diagonally dominant infinite matrices. II
• Minimal Gerschgorin sets
• Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices
• Spectral properties of diagonally dominant infinite matrices, part I
• Eigenvalues of infinite matrices
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Minimal Gerschgorin Sets for Partitioned Matrices

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