Jordan canonical form application to differential equations /

• Main Author: Weintraub, Steven H.
• Format: Electronic
• Language: English
• Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008.
• Series: Synthesis lectures on mathematics and statistics (Online) ; #2.
• Subjects: Jordan matrix.; Differential equations.
• Online Access: Abstract with links to full text
• Item Description: Part of: Synthesis digital library of engineering and computer science.; Title from PDF t.p. (viewed on October 15, 2008).; Series from website.; Includes index.
• Physical Description: 1 electronic text (viii, 85 p. : ill.) : digital file.; Also available in print.
• Format: Mode of access: World Wide Web.; System requirements: Adobe Acrobat Reader.
• ISBN: 9781598298055 (electronic bk.); 9781598298048 (pbk.)
• Access: Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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).