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Jordan canonical form application to differential equations by Steven H. Weintraub

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Published by Morgan & Claypool Publishers in San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) .
Written in English

Subjects:

  • Jordan matrix,
  • Differential equations

Book details:

About the Edition

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).

Edition Notes

Other titlesSynthesis digital library of engineering and computer science.
StatementSteven H. Weintraub
SeriesSynthesis lectures on mathematics and statistics -- #2
Classifications
LC ClassificationsQA371 .W455 2008
The Physical Object
Format[electronic resource] :
ID Numbers
Open LibraryOL27065784M
ISBN 109781598298055, 9781598298048

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Jordan canonical form 12–2 • J is upper bidiagonal • J diagonal is the special case of n Jordan blocks of size n i = 1 • Jordan form is unique (up to permutations of the blocks). Preface Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in JCF of a linear transformation,or of a matrix,encodes all of the structural information about that linear transformation, or book is a careful development of JCF. / Mathematics Books / Geometry Books / Algebraic Geometry Books / Jordan Canonical Form. Jordan Canonical Form. Jordan Canonical Form. Currently this section contains no detailed description for the page, will update this page soon. Author(s): NA. NA Pages. Download / View book. Similar Books. I am currently reading the book Basic Algebra [modern] Anthony W. Knapp about Jordan canonical form. Is there any detailed oriented book about Jordan Normal Form which explain. An Algorithm to put a matrix in Jordan normal form. How to Find Bases for Jordan Canonical Forms (i think there is lots but one which universal based on proof).

in Jordan canonical form. Doing this for each gives a Jordan canonical form basis for V. If the above is intimidating, don't worry; this is usually best seen with examples. One thing that helps is if you know a Jordan canonical form (eg by the method from the last pdf), you know how many chains to look for and what length they Size: KB. A proof of the Jordan normal form theorem Jordan normal form theorem states that any matrix is similar to a block-diagonal matrix with Jordan blocks on the diagonal. To prove it, we rst reformulate it in the following way: Jordan normal form theorem. For any nite-dimensional vector space V and any linear operator A: V! V, there exist. In linear algebra, a Jordan normal form, also known as a Jordan canonical form or JCF, is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal, and with identical diagonal entries to the left and . A SHORT PROOF OF THE EXISTENCE OF JORDAN NORMAL FORM MARK WILDON Let V be a finite-dimensional complex vector space and let T: V → V be a linear map. A fundamental theorem in linear algebra asserts that there is a basis of V in which T is represented by a matrix in Jordan normal form.

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. 5into Jordan canonical form. 1) Then you can check that = 1 is the only eigenvalue of A. 2) Nul(A I) = Span 8 Jordan canonical forms: 2 4 File Size: KB. Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. Jordan form is unique. A diagonal matrix is in Jordan form. Thus the Jordan form of a diagonalizable matrix is its diagonalization. If the minimal polynomial has factors to some power higher than one then the Jordan form has subdiagonal 's, and so is not diagonal.