Schur complements and its applications to symmetric nonnegative and \(Z\)-matrices

DOI10.1016/S0024-3795(02)00327-0zbMath1006.15020MaRDI QIDQ697067

Yi-Zheng Fan

Publication date: 12 September 2002

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

zbMATH Keywords

Schur complementnonnegative matricesPerron complement\(Z\)-matriceseigenvalues interlacing

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (5)

Localization of Perron roots ⋮ Smooth over-parameterized solvers for non-smooth structured optimization ⋮ The lower and upper bounds on Perron root of nonnegative irreducible matrices ⋮ A Schur complement approach for computing subcovariance matrices arising in a road safety measure modelling ⋮ A covariance components estimation procedure when modelling a road safety measure in terms of linear constraints

Cites Work

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• On the second real eigenvalue of nonegative and Z-matrices
• Inverse \(N_ 0\)-matrices
• Some notes on Z-matrices
• Uncoupling the Perron eigenvector problem
• A generalization of N-matrices
• A classification of matrices of class Z
• Lower bounds for the first eigenvalue of certain M-matrices associated with graphs
• Some interlacing properties of the Schur complement of a Hermitian matrix
• \(Z\)-matrices and inverse \(Z\)-matrices
• Bounds on eigenvalues and chromatic numbers
• Inverses of Perron complements of inverse \(M\)-matrices
• Some results on a partition of \(Z\)-matrices
• Matrix Analysis
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems
• Generalized Inverse Formulas Using the Schur Complement
• An Identity for the Schur Complement of a Matrix

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