On \(p\)th roots of stochastic matrices

DOI10.1016/j.laa.2010.04.007zbMath1223.15042OpenAlexW2118918399WikidataQ56998709 ScholiaQ56998709MaRDI QIDQ541909

Lijing Lin, Nicholas J. Higham

Publication date: 8 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.04.007

zbMATH Keywords

\(M\)-matrixMarkov chainnonnegative matricesstochastic matricesinverse eigenvalue problemembeddabilitytransition matricesmatrix \(p\)th rootmatrix function

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Stochastic matrices (15B51) Matrix exponential and similar functions of matrices (15A16)

Related Items

Nonnegative square roots of matrices, Embeddability of real and positive operators, The complexity of divisibility, On the positive semi-definite pth roots of positive semi-definite doubly stochastic matrices, On equal-input and monotone Markov matrices, Roots of completely positive maps, Matrix roots and embedding conditions for three-state discrete-time Markov chains with complex eigenvalues, Infinitely divisible nonnegative matrices, \(M\)-matrices, and the embedding problem for finite state stationary Markov chains, Structured level-2 condition numbers of matrix functions, The upper density of an automatic set is rational, Unnamed Item, Factorization of matrices with symmetries over function algebras, Pauli semigroups and unistochastic quantum channels, Matrix roots in the max-plus algebra, Matrix roots of eventually positive matrices, Structure preserving matrix means on the Marcus-Minc stochastic matrices, Some Results on the Embeddable Problem for Discrete-Time Markov Models in Manpower Planning, Sufficient embedding conditions for three-state discrete-time Markov chains with real eigenvalues, On monotone Markov chains and properties of monotone matrix roots, On the use of Cauchy integral formula for the embedding problem of discrete-time Markov chains

Uses Software

• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding Generators for Markov Chains via Empirical Transition Matrices, with Applications to Credit Ratings
• Embeddable Markov matrices
• On Newton's method and Halley's method for the principal \(p\)th root of a matrix
• A Schur method for the square root of a matrix
• Structure of the \(n\)th roots of a matrix
• Modifying the inertia of matrices arising in optimization
• A family of matrices, the discretized Brownian bridge, and distance-based regression
• Orthogonal bases that leads to symmetric nonnegative matrices
• Nonnegative matrices with stochastic powers
• On single and double Soules matrices
• Algorithms for the matrix \(p\)th root
• Spectral properties of doubly-stochastic matrices
• On the m-th roots of a complex matrix
• Analytic functions ofM-matrices and generalizations
• Some Results on Doubly Stochastic Matrices
• On the Newton Method for the Matrix Pth Root
• A Family of Rational Iterations and Its Application to the Computation of the Matrix pth Root
• Constructing symmetric nonnegative matrices
• Matrix Analysis
• On the characteristic roots of matrices with nonnegative elements
• Inverse of Strictly Ultrametric Matrices are of Stieltjes Type
• A Linear Algebra Proof that the Inverse of a Strictly Ultrametric Matrix is a Strictly Diagonally Dominant Stieltjes Matrix
• A Schur Algorithm for Computing Matrix pth Roots
• A Schur–Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse
• Functions of Matrices
• An intrinsic time for non-stationary finite markov chains
• The imbedding problem for finite Markov chains
• A binary powering Schur algorithm for computing primary matrix roots