Jordan Canonical Form Application to Differential Equations: Jordan Canonical Form Application to Differential Equations.pdf

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Jordan Canonical Form: Application to Differential Equations
Steven H.Weintraub
www.morganclaypool.com
ISBN: 9781598298048 paperback
ISBN: 9781598298055 ebook
DOI 10.2200/S00146ED1V01Y200808MAS002
A Publication in the Morgan & Claypool Publishers series
SYNTHESIS LECTURES ONMATHEMATICS AND STATISTICS
Lecture #2
Series Editor: Steven G. Krantz,Washington University, St. Louis
Series ISSN
Synthesis Lectures on Mathematics and Statistics
ISSN pending.

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .v
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Jordan Canonical Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 The Diagonalizable Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
2 Solving Systems of Linear Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
2.1 Homogeneous Systems with Constant Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . .25
2.2 Homogeneous Systems with Constant Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . .40
2.3 Inhomogeneous Systems with Constant Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 The Matrix Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
A Background Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
A.1 Bases, Coordinates, and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
A.2 Properties of the Complex Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B Answers to Odd-Numbered Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85

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