Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues

DOI10.1016/0024-3795(94)00301-SzbMath0833.15004WikidataQ127186405 ScholiaQ127186405MaRDI QIDQ1893088

Michael Neumann, Stephen J. Kirkland

Publication date: 3 July 1995

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

zbMATH Keywords

eigenvaluesMATLABsingular valuesmagic squaresgroup generalized inversesingular irreducible \(M\)-matricesdoubly regular tournament matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Orthogonal arrays, Latin squares, Room squares (05B15) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (10)

\(M\)-matrix generalized inverses of \(M\)-matrices ⋮ Boundary Value Problems on Finite Networks ⋮ The \(M\)-matrix group inverse problem for distance-biregular graphs ⋮ On properties of special magic square matrices ⋮ Matrices whose group inverses are \(M\)-matrices ⋮ Spectra of order-4 special magic squares ⋮ Unnamed Item ⋮ Some stochastic properties of ``semi-magic and ``magic Markov chains ⋮ Magic square spectra ⋮ Distance–regular graphs having theM-property

Uses Software

• Matlab

Cites Work

• Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix
• On convexity properties of the spectral radius of nonnegative matrices
• On the first and second order derivatives of the Perron vector
• Algebraic multiplicity of the eigenvalues of a tournament matrix
• Taylor expansions of eigenvalues of perturbed matrices with applications to spectral radii of nonnegative matrices
• Nonnegative alternating circulants leading to \(M\)-matrix group inverses
• Random evolutions and the spectral radius of a non-negative matrix
• Construction of a set of test matrices
• Using the QR Factorization and Group Inversion to Compute, Differentiate, and Estimate the Sensitivity of Stationary Probabilities for Markov Chains
• Derivatives and Perturbations of Eigenvectors
• Shorter Notes: Convexity of the Dominant Eigenvalue of an Essentially Nonnegative Matrix
• Convex spectral functions
• The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Derivatives of the spectral radius as a function of non-negative matrix elements
• Convexity and Concavity of the Perron Root and Vector of Leslie Matrices with Applications to a Population Model
• A Remark on Characteristic Polynomials
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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