Nonhomogeneous Matrix Products
by Hartfiel, Darald J.Format: Hardcover
Pub. Date: 2002-01-01
Publisher(s): WORLD SCIENTIFIC PUB CO INC
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Summary
Puts together much of the basic work on infinite products of matrices, providing a primary source for such work.
Author Biography
Darald J. Hartfiel received his Ph.D. degree in mathematics from the University of Houston in 1969. Since then, he has been on the faculty of Texas A&M University. Professor Hartfiel has written 97 research papers, mostly in matrix theory and related areas. He is the author of three books, one of which is a monograph
Table of Contents
| Preface | p. v |
| Introduction | p. 1 |
| Functionals | p. 5 |
| Projective and Hausdorff Metrics | p. 5 |
| Projective Metric | p. 5 |
| Hausdorff Metric | p. 14 |
| Contraction Coefficients | p. 18 |
| Birkhoff Contraction Coefficient | p. 19 |
| Subspace Contraction Coefficient | p. 27 |
| Blocking | p. 32 |
| Measures of Irreducibility and Full Indecomposability | p. 33 |
| Spectral Radius | p. 38 |
| Research Notes | p. 42 |
| Semigroups of Matrices | p. 45 |
| Limiting Sets | p. 46 |
| Algebraic Properties | p. 46 |
| Convergence Properties | p. 49 |
| Bounded Semigroups | p. 54 |
| Research Notes | p. 58 |
| Patterned Matrices | p. 59 |
| Scrambling Matrices | p. 59 |
| Sarymsakov Matrices | p. 64 |
| Research Notes | p. 68 |
| Ergodicity | p. 71 |
| Birkhoff Coefficient Results | p. 71 |
| Direct Results | p. 78 |
| Research Notes | p. 85 |
| Convergence | p. 87 |
| Reduced Matrices | p. 87 |
| Convergence to 0 | p. 91 |
| Results on [Pi](U[subscript k] + A[subscript k]) | p. 98 |
| Joint Eigenspaces | p. 103 |
| Research Notes | p. 105 |
| Continuous Convergence | p. 107 |
| Sequence Spaces and Convergence | p. 107 |
| Canonical Forms | p. 110 |
| Coefficients and Continuous Convergence | p. 114 |
| Research Notes | p. 116 |
| Paracontracting | p. 117 |
| Convergence | p. 118 |
| Types of Trajectories | p. 122 |
| Research Notes | p. 130 |
| Set Convergence | p. 133 |
| Bounded Semigroups | p. 133 |
| Contraction Coefficient Results | p. 136 |
| Birkhoff Coefficient Results | p. 136 |
| Subspace Coefficient Results | p. 138 |
| Convexity in Convergence | p. 139 |
| Research Notes | p. 142 |
| Perturbations in Matrix Sets | p. 143 |
| Subspace Coefficient Results | p. 143 |
| Birkhoff Coefficient Results | p. 145 |
| Research Notes | p. 150 |
| Graphics | p. 151 |
| Maps | p. 151 |
| Graphing Curves | p. 152 |
| Graphing Fractals | p. 157 |
| Research Notes | p. 162 |
| MATLAB Codes | p. 163 |
| Slowly Varying Products | p. 167 |
| Convergence to 0 | p. 167 |
| Estimates of x[subscript k] from Current Matrices | p. 174 |
| State Estimates from Fluctuating Matrices | p. 179 |
| Fluctuations | p. 180 |
| Normalized Trajectories | p. 182 |
| Fluctuation Set | p. 183 |
| Quotient Spaces | p. 187 |
| Norm on R[superscript n] / W | p. 188 |
| Matrices in R[superscript n] / W | p. 190 |
| Behavior of Trajectories | p. 193 |
| Research Notes | p. 198 |
| Systems | p. 199 |
| Projective Maps | p. 199 |
| Demographic Problems | p. 201 |
| Business, Man Power, Production Systems | p. 204 |
| Research Notes | p. 211 |
| MATLAB Codes | p. 212 |
| Appendix | p. 215 |
| Bibliography | p. 217 |
| Index | p. 223 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
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