rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Group inverses of M-matrices and their applications
  name:
    name part: Kirkland, Stephen J.
    role:
      role term: creator
  name:
    name part: Neumann, Michael
    name part: 1946 November 23-
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    place:
      place term: Boca Raton
    publisher: CRC Press
    date issued: ©2013
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xv, 311 pages) : illustrations
  abstract: "Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas."--Publisher's website.
  table of contents: Motivation and Examples -- The Group Inverse -- Group Inverses and Derivatites of Matrix Functions -- Perron Eigenpair in Demographic Applications -- The Group Inverse in Markov Chains -- Mean First Passage Times for Markov Chains -- Applications of the Group Inverse to Laplacian Matrices -- Computing the Group Inverse.
  note: Stephen J. Kirkland, Michael Neumann.
  note: Includes bibliographical references.
  note: English.
  subject:
    topic: Matrices
  subject:
    topic: Inverse problems (Differential equations)
  subject:
    topic: Matrices
  subject:
    topic: Problèmes inverses (Équations différentielles)
  subject:
    topic: MATHEMATICS
    topic: Matrices
  subject:
    topic: Mathematics
  subject:
    topic: Inverse problems (Differential equations)
  subject:
    topic: Matrices
  classification: QA188 .K57 2013eb
  classification: 512.9434
  related item:
    title info:
      title: Group inverses of M-matrices and their applications
    name:
      name part: Kirkland, Stephen J.
    origin info:
      publisher: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2013]
    identifier: (DLC) 2012554485
    identifier: (OCoLC)829009978
  related item:
    title info:
      title: Chapman & Hall/CRC applied mathematics and nonlinear science series
  identifier: 9781439888599
  identifier: 1439888590
  identifier: 9781439888582
  identifier: 1439888582
  identifier: 0429111045
  identifier: 9780429111044
  identifier: TANDF_249307 Ingram Content Group
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: E7B
    record creation date: 130212
    record change date: 20241111204752.1
    record identifier: in00005528160
    language of cataloging:
      language term: eng