非齐次矩阵积/NONHOMOGENEOUS MATRIX PRODUCTS

书籍目录

Preface1  Introduction 2  Functionals  2.1  Projective and Hausdorff Metrics     2.1.1  Projective Metric     2.1.2  Hausdorff Metric  2.2  Contraction Coefficients     2.2.1  Birkhoff Contraction Coefficient     2.2.2  Subspace Contraction Coefficient     2.2.3  Blocking  2.3  Measures of Irreducibility and ~11 Indecomposability  2.4  Spectral Radius  2.5  Research Notes3  Semigroups of Matrices  3.1  Limiting Sets     3.1.1  Algebraic Properties     3.1.2  Convergence Properties  3.2  Bounded Semigroups  3.3  Research Notes4  Patterned Matrices  4.1  Scrambling Matrices  4.2  Sarymsakov Matrices  4.3  Research Notes5  Ergodicity  5.1  Birkhoff Coefficient Results  5.2  Direct Results  5.3  Research Notes6  Convergence  6.1  Reduced Matrices  6.2  Convergence to 0  6.3  Results on II (Uk + A~)  6.4  Joint Eigenspaces  6.5  Research Notes7  Continuous Convergence  7.1  Sequence Spaces and Convergence  7.2  Canonical Forms  7.3  Coefficients and Continuous Convergence  7.4  Research Notes8  Paracontracting  8.1  Convergence  8.2  Types of Trajectories  8.3  Research Notes9  Set Convergence10  Perturbations in Matrix Sets11  Graphics12  Slowly Varying Products13  SystemsAppendixBibliographyIndex

作者简介

Infinite products of matrices are used in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata, production and manpower systems, tomography, and fractals. More recent results have been obtained in computer design of curves and surfaces. This study puts together much of the basic work on infinite products of matrices, providing a primary source for such work. This should eliminate the rediscovery of known results in the area, and thus save considerable time for researchers who work with infinite products of matrices. In addition, two chapters are included to show how infinite products of matrices are used in graphics and in systems work.

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