| Preface |
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xi | |
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1 | (6) |
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Some Notation and Terminology |
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1 | (2) |
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3 | (1) |
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Inner Products and Orthogonality |
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4 | (1) |
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4 | (3) |
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7 | (10) |
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7 | (2) |
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9 | (1) |
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10 | (3) |
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Sums and Intersections of Subspaces |
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13 | (4) |
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17 | (12) |
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17 | (1) |
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Matrix Representation of Linear Transformations |
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18 | (1) |
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Composition of Transformations |
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19 | (1) |
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Structure of Linear Transformations |
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20 | (2) |
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Four Fundamental Subspaces |
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22 | (7) |
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Introduction to the Moore--Penrose Pseudoinverse |
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29 | (6) |
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Definitions and Characterizations |
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29 | (1) |
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30 | (1) |
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Properties and Applications |
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31 | (4) |
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Introduction to the Singular Value Decomposition |
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35 | (8) |
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35 | (3) |
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38 | (2) |
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Row and Column Compressions |
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40 | (3) |
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43 | (8) |
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43 | (1) |
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44 | (3) |
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A More General Matrix Linear Equation |
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47 | (1) |
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Some Useful and Interesting Inverses |
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47 | (4) |
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Projections, Inner Product Spaces, and Norms |
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51 | (14) |
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51 | (3) |
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The four fundamental orthogonal projections |
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52 | (2) |
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54 | (3) |
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57 | (2) |
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59 | (6) |
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Linear Least Squares Problems |
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65 | (10) |
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The Linear Least Squares Problem |
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65 | (2) |
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67 | (1) |
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Linear Regression and Other Linear Least Squares Problems |
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67 | (3) |
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Example: Linear regression |
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67 | (2) |
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Other least squares problems |
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69 | (1) |
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Least Squares and Singular Value Decomposition |
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70 | (1) |
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Least Squares and QR Factorization |
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71 | (4) |
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Eigenvalues and Eigenvectors |
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75 | (20) |
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Fundamental Definitions and Properties |
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75 | (7) |
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82 | (3) |
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85 | (4) |
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86 | (2) |
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On the +1's in JCF blocks |
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88 | (1) |
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Geometric Aspects of the JCF |
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89 | (2) |
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91 | (4) |
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95 | (14) |
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Some Basic Canonical Forms |
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95 | (4) |
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99 | (3) |
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Equivalence Transformations and Congruence |
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102 | (2) |
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Block matrices and definiteness |
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104 | (1) |
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104 | (5) |
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Linear Differential and Difference Equations |
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109 | (16) |
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109 | (9) |
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Properties of the matrix exponential |
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109 | (3) |
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Homogeneous linear differential equations |
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112 | (1) |
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Inhomogeneous linear differential equations |
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112 | (1) |
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Linear matrix differential equations |
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113 | (1) |
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114 | (1) |
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Computation of the matrix exponential |
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114 | (4) |
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118 | (2) |
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Homogeneous linear difference equations |
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118 | (1) |
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Inhomogeneous linear difference equations |
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118 | (1) |
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Computation of matrix powers |
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119 | (1) |
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120 | (5) |
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Generalized Eigenvalue Problems |
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125 | (14) |
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The Generalized Eigenvalue/Eigenvector Problem |
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125 | (2) |
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127 | (3) |
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Application to the Computation of System Zeros |
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130 | (1) |
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Symmetric Generalized Eigenvalue Problems |
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131 | (2) |
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Simultaneous Diagonalization |
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133 | (2) |
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Simultaneous diagonalization via SVD |
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133 | (2) |
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Higher-Order Eigenvalue Problems |
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135 | (4) |
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Conversion to first-order form |
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135 | (4) |
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139 | (12) |
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139 | (1) |
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Properties of the Kronecker Product |
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140 | (4) |
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Application to Sylvester and Lyapunov Equations |
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144 | (7) |
| Bibliography |
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151 | (2) |
| Index |
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153 | |