Analytic functions ofM-matrices and generalizations

DOI10.1080/03081088308817519zbMath0525.15012OpenAlexW1981441499MaRDI QIDQ3039496

Miroslav Fiedler, Hans Schneider

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/03081088308817519

zbMATH Keywords

matrix rootsM-matricesZ-matricesanalytic functions of matrices

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Functional calculus for linear operators (47A60)

Related Items

Positive cones and convergence conditions for iterative methods based on splittings ⋮ On the positive semi-definite pth roots of positive semi-definite doubly stochastic matrices ⋮ Closure properties of certain positivity classes of matrices under various algebraic operations ⋮ On square roots of \(M\)-operators ⋮ On Newton's method and Halley's method for the principal \(p\)th root of a matrix ⋮ Monotonicity and positivity of coefficients of power series expansions associated with Newton and Halley methods for the matrix \(p\)th root ⋮ Nonnegative Solutions of a Quadratic Matrix Equation Arising from Comparison Theorems in Ordinary Differential Equations ⋮ Infinitely divisible nonnegative matrices, \(M\)-matrices, and the embedding problem for finite state stationary Markov chains ⋮ On \(p\)th roots of stochastic matrices ⋮ A study of Schröder's method for the matrix \(p\)th root using power series expansions ⋮ On functions that preserve M-matrices and inverse M-matrices ⋮ Inverse \(M\)-matrix, a new characterization ⋮ Notes on \(\omega\)- and \(\tau\)-matrices

Cites Work

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• On square roots of M-matrices
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• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Nonnegatively posed problems and completely monotonic functions
• Über die Determinanten mit überwiegender Hauptdiagonale
• Inequalities for M-matrices
• What is the Laplace Transform?