CRC Press, Taylor & Francis Group, 2013. — 330 p. — (Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series). — ISBN-10 1439888582.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.… 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. Contents Motivation and Examples The Group Inverse Group Inverses and Derivatives of Matrix 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
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