On the first and second order derivatives of the Perron vector

DOI10.1016/0024-3795(85)90235-6zbMath0578.15018OpenAlexW2068042605MaRDI QIDQ1066237

Emeric Deutsch, Michael Neumann

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0024-3795(85)90235-6

zbMATH Keywords

convexityrootPerron vectorPerronsecond derivativenonnegative irreducible matrixgroup generalized inverse

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (22)

The evolutionary reduction principle for linear variation in genetic transmission ⋮ Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues ⋮ Nonnegative alternating circulants leading to \(M\)-matrix group inverses ⋮ On algebraic connectivity as a function of an edge weight ⋮ Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models ⋮ On the derivative of the Perron vector whose infinity norm is fixed ⋮ Number of source patches required for population persistence in a source-sink metapopulation with explicit movement ⋮ An iterative algorithm for computing mean first passage times of Markov chains ⋮ Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems ⋮ Stochastic analysis of the motion of DNA nanomechanical bipeds ⋮ Perron vector optimization applied to search engines ⋮ Improved bounds for a condition number for Markov chains ⋮ An extrapolation method for computing derivatives of eigensystems ⋮ Logarithmic Convexity of Perron-Frobenius Eigenvectors of Positive Matrices ⋮ Resolvent positive linear operators exhibit the reduction phenomenon ⋮ Networks, Information and Choice ⋮ Impact of Varying Community Networks on Disease Invasion ⋮ Proximity in group inverses of M-matrices and inverses of diagonally dominant M-matrices ⋮ Markov chain sensitivity measured by mean first passage times ⋮ Regular Markov chains for which the transition matrix has large exponent ⋮ Sharp Entrywise Perturbation Bounds for Markov Chains ⋮ Probabilistic approach to Perron root, the group inverse, and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix
• Resolvent expansions of matrices and applications
• Non-negative matrices and Markov chains. 2nd ed
• More on generalizations of matrix monotonicity
• The Effect of the Perturbation of Hermitian Matrices on their Eigenvectors
• On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• A Hadamard product involving N-matrices
• Derivatives of the spectral radius as a function of non-negative matrix elements
• Diagonally dominant matrices

This page was built for publication: On the first and second order derivatives of the Perron vector