Group Inverses of M-Matrices and Their Applications: 26 (Chapman & Hall/CRC Applied Mathematics and Nonlinear Science)

Book Details
• Format: Hardcover
• Language: English
• Pages: 332
• Writer: Stephen J. Kirkland
• Publisher: CRC Press
• Edition: 1
• Binding: Hardcover
• EAN: 9781439888582
• Package Dimensions: 9.3 x 6.2 x 0.9 inches

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 book develops the basic algebraic and spectral properties of the group inverse of a general matrix. It then derives formulas for derivatives of matrix functions and applies them to matrices arising in demographic settings, including the class of Leslie matrices. With a focus on Markov chains, it shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector and in deriving a bound for the asymptotic convergence rate of the Markov chain. It also illustrates the use of 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 connections between problems in Markov chains, Perron eigenvalue analysis, and spectral graph theory, demonstrating how group inverses provide valuable insights across these areas.