Jordan canonical form
Subtitle: application to differential equations
By: Steven H. Weintraub
Series: Synthesis lectures on mathematics and statistics -- #2
Publisher: Morgan & Claypool Publishers
Published: 2008
Place of publication: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA)
Language: eng
Format: [electronic resource] :
ISBN-13: 9781598298055; 9781598298048
Subjects: Jordan matrix; Differential equations
Other titles: Synthesis digital library of engineering and computer science.
Description: Jordan Canonical Form ( JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it-eigenvalues, eigenvectors, and chains of generalized eigenvectors. We begin with the diagonalizable case and then proceed to the general case, but we do not present a complete proof. Indeed, our interest here is not in JCF per se, but in one of its important applications. We devote the bulk of our attention in this book to showing how to apply JCF to solve systems of constant-coefficient first order differential equations, where it is a very effective tool. We cover all situations-homogeneous and inhomogeneous systems; real and complex eigenvalues. We also treat the closely related topic of the matrix exponential. Our discussion is mostly confined to the 2-by-2 and 3-by-3 cases, and we present a wealth of examples that illustrate all the possibilities in these cases (and of course, a wealth of exercises for the reader).
Notes: Part of: Synthesis digital library of engineering and computer science.

Title from PDF t.p. (viewed on October 15, 2008).

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Includes index.

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Table of contents: title: Jordan canonical form; title: The diagonalizable case; title: The general case; title: Solving systems of linear differential equations; title: Homogeneous systems with constant coefficients; title: Homogeneous systems with constant coefficients; title: Inhomogeneous systems with constant coefficients; title: The matrix exponential; title: Background results; title: A.1. Bases, coordinates, and matrices; title: A.2. Properties of the complex exponential; title: B. Answers to odd-numbered exercises.