عنوان

Jordan canonical form :

1598298054

9781598298055

1598298046

9781598298048

b744032

Jordan canonical form :

[Book]

application to differential equations /

Steven H. Weintraub.

[San Rafael, CA] :

Morgan & Claypool Publishers,

©2008.

1 online resource (viii, 85 pages)

Synthesis lectures on mathematics and statistics ;

#2

Includes index.

Title from PDF title page (viewed Nov. 6, 2008).

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.

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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).

01307586

Jordan canonical form.

9781598298048

Algebras, Linear.

Jordan algebras.

Algebras, Linear.

Jordan algebras.

MATHEMATICS-- Differential Equations-- General.

MAT-- 007000

Weintraub, Steven H.

20201204043000.0

pn

[Book]

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