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| Preface to the Dover Edition | |
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| Preface | |
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| A Sketch of Some Matrix Theory | |
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| Definitions | |
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| Column and Row Vectors | |
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| Square Matrices | |
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| Linear Dependence, Rank, and Degeneracy | |
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| Special Kinds of Matrices | |
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| Matrices Dependent on a Scalar Parameter; Latent Roots and Vectors | |
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| Eigenvalues and Vectors | |
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| Equivalent Matrices and Similar Matrices | |
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| The Jordan Canonical Form | |
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| Bounds for Eigenvalues | |
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| Regular Pencils of Matrices and Eigenvalue Problems | |
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| Introduction | |
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| Orthogonality Properties of the Latent Vectors | |
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| The Inverse of a Simple Matrix Pencil | |
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| Application to the Eigenvalue Problem | |
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| The Constituent Matrices | |
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| Conditions for a Regular Pencil to be Simple | |
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| Geometric Implications of the Jordan Canonical Form | |
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| The Rayleigh Quotient | |
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| Simple Matrix Pencils with Latent Vectors in Common | |
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| Lambda-Matrices, I | |
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| Introduction | |
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| A Canonical Form for Regular [lambda]-Matrices | |
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| Elementary Divisors | |
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| Division of Square [lambda]-Matrices | |
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| The Cayley-Hamilton Theorem | |
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| Decomposition of [lambda]-Matrices | |
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| Matrix Polynomials with a Matrix Argument | |
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| Lambda-Matrices, II | |
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| Introduction | |
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| An Associated Matrix Pencil | |
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| The Inverse of a Simple [lambda]-Matrix in Spectral Form | |
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| Properties of the Latent Vectors | |
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| The Inverse of a Simple [lambda]-Matrix in Terms of its Adjoint | |
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| Lambda-matrices of the Second Degree | |
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| A Generalization of the Rayleigh Quotient | |
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| Derivatives of Multiple Eigenvalues | |
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| Some Numerical Methods for Lambda-matrices | |
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| Introduction | |
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| A Rayleigh Quotient Iterative Process | |
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| Numerical Example for the RQ Algorithm | |
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| The Newton-Raphson Method | |
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| Methods Using the Trace Theorem | |
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| Iteration of Rational Functions | |
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| Behavior at Infinity | |
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| A Comparison of Algorithms | |
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| Algorithms for a Stability Problem | |
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| Illustration of the Stability Algorithms | |
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| Appendix to Chapter 5 | |
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| Ordinary Differential Equations with Constant Coefficients | |
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| Introduction | |
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| General Solutions | |
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| The Particular Integral when f(t) is Exponential | |
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| One-point Boundary Conditions | |
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| The Laplace Transform Method | |
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| Second Order Differential Equations | |
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| The Theory of Vibrating Systems | |
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| Introduction | |
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| Equations of Motion | |
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| Solutions under the Action of Conservative Restoring Forces Only | |
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| The Inhomogeneous Case | |
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| Solutions Including the Effects of Viscous Internal Forces | |
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| Overdamped Systems | |
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| Gyroscopic Systems | |
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| Sinusoidal Motion with Hysteretic Damping | |
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| Solutions for Some Non-conservative Systems | |
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| Some Properties of the Latent Vectors | |
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| On the Theory of Resonance Testing | |
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| Introduction | |
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| The Method of Stationary Phase | |
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| Properties of the Proper Numbers and Vectors | |
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| Determination of the Natural Frequencies | |
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| Determination of the Natural Modes | |
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| Appendix to Chapter 8 | |
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| Further Results for Systems with Damping | |
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| Preliminaries | |
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| Global Bounds for the Latent Roots when B is Symmetric | |
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| The Use of Theorems on Bounds for Eigenvalues | |
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| Preliminary Remarks on Perturbation Theory | |
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| The Classical Perturbation Technique for Light Damping | |
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| The Case of Coincident Undamped Natural Frequencies | |
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| The Case of Neighboring Undamped Natural Frequencies | |
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| Bibliographical Notes | |
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| References | |
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| Index | |