Composite matrix inverses and generalized Gershgorin sets

DOI10.1017/S0305004100061533zbMath0546.15005OpenAlexW2092367589MaRDI QIDQ3337596

Osita D. I. Nwokhah

Publication date: 1984

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100061533

zbMATH Keywords

block partitioned matricesM-matriceseigenvalue inclusionGershgorin circlesblock eigenvalue estimationsblock partitioned Nyquist method

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48)

Cites Work

• Estimates for the inverse of a matrix and bounds for eigenvalues
• Note on circular disks containing the eigenvalues of a matrix
• Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem
• Estimates for the inverse of a matrix
• A complex variable approach to the analysis of linear multivariable feedback systems
• Gershgorin domains for partitioned matrices
• Über die Determinanten mit überwiegender Hauptdiagonale
• Limits for the characteristic roots of a matrix
• The convergence and local minimality of bounds for transfer functions
• A generalized Nyquist-type stability criterion for multivariable feedback systems†
• Geršgorin Theorems, Regularity Theorems, and Bounds for Determinants of Partitioned Matrices
• Note on Bounds for Determinants with Dominant Principal Diagonal

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