Jordan canonical form : application to differential equations /
By: Weintraub, Steven H.
Material type:
BookSeries: Synthesis lectures on mathematics and statistics: #2.Publisher: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008Description: 1 electronic text (viii, 85 p. : ill.) : digital file.ISBN: 9781598298055 (electronic bk.); 9781598298048 (pbk.).Uniform titles: Synthesis digital library of engineering and computer science. Subject(s): Jordan matrix | Differential equations | Jordan Canonical Form | Linear algebra | Differential equations | Eigenvalues | Eigenvectors | Generalized eigenvectors | Matrix exponentialDDC classification: 515.35 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
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PK Kelkar Library, IIT Kanpur | Available | EBKE118 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Series from website.
Includes index.
Jordan canonical form -- The diagonalizable case -- The general case -- Solving systems of linear differential equations -- Homogeneous systems with constant coefficients -- Homogeneous systems with constant coefficients -- Inhomogeneous systems with constant coefficients -- The matrix exponential -- Background results -- A.1. Bases, coordinates, and matrices -- A.2. Properties of the complex exponential -- B. Answers to odd-numbered exercises.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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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).
Also available in print.
Title from PDF t.p. (viewed on October 15, 2008).
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