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Books > Science & Mathematics > Mathematics > Algebra
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Group Inverses of M-Matrices and Their Applications (Paperback)
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Group Inverses of M-Matrices and Their Applications (Paperback)
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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.
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