非齐次矩阵积/NONHOMOGENEOUS MATRIX PRODUCTS

2002-1  

Pengiun Group (USA)  

Hartfiel, Darald J.  

224  

Infinite products of matrices are used in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata,production and manpower systems, tomography, and fractals. Morerecent results have been obtained in computer design of curves andsurfaces. This book puts together much of the basic work on infinite products of matrices, providing a primary source for such work. This will 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.

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

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