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cr cn |||m|||a |
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090909s2009 caua fsa 001 0 eng d |
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|a 9781608452514 (electronic bk.)
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|z 9781608452507 (pbk.)
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|a 10.2200/S00218ED1V01Y200908MAS006
|2 doi
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|a (CaBNvSL)gtp00535641
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|a CaBNvSL
|c CaBNvSL
|d CaBNvSL
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|a QA252.5
|b .W455 2009
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|a 512.24
|2 22
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|a Weintraub, Steven H.
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|a Jordan Canonical Form
|b theory and practice /
|c Steven H. Weintraub.
|h [electronic resource] :
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|a San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) :
|b Morgan & Claypool Publishers,
|c c2009.
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| 300 |
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|a 1 electronic text (x, 96 p. : ill.) :
|b digital file.
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| 490 |
1 |
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|a Synthesis lectures on mathematics and statistics,
|v # 6
|x 1938-1751 ;
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| 500 |
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|a Part of: Synthesis digital library of engineering and computer science.
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| 500 |
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|a Title from PDF t.p. (viewed on September 9, 2009).
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|a Series from website.
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|a Includes index.
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|a 1. Fundamentals on vector spaces and linear transformations -- Bases and coordinates -- Linear transformations and matrices -- Some special matrices -- Polynomials in T and A -- Subspaces, complements, and invariant subspaces -- 2. The structure of a linear transformation -- Eigenvalues, eigenvectors, and generalized eigenvectors -- The minimum polynomial -- Reduction to BDBUTCD form -- The diagonalizable case -- Reduction to Jordan Canonical Form -- Exercises -- 3. An algorithm for Jordan Canonical Form and Jordan Basis -- The ESP of a linear transformation -- The algorithm for Jordan Canonical Form -- The algorithm for a Jordan Basis -- Examples -- Exercises -- A. Answers to odd-numbered exercises -- Notation -- Index.
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|a Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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|a Compendex
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|a INSPEC
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|a Google scholar
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|a Google book search
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|a 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. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials.We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finite-dimensional vector space over the field of complex numbers C, and let T : V -. V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: Let A be a square matrix with complex entries. Then A is similar to a matrix J in Jordan Canonical Form, i.e., there is an invertible matrix P and a matrix J in Jordan Canonical Form with A = PJP-1.We further present an algorithm to find P and J , assuming that one can factor the characteristic polynomial of A. In developing this algorithm we introduce the eigenstructure picture (ESP) of a matrix, a pictorial representation that makes JCF clear. The ESP of A determines J , and a refinement, the labelled eigenstructure picture (ESP) of A, determines P as well.We illustrate this algorithm with copious examples, and provide numerous exercises for the reader.
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|a Also available in print.
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|a Mode of access: World Wide Web.
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|a System requirements: Adobe Acrobat reader.
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| 650 |
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|a Jordan algebras.
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| 650 |
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|a Algebras, Linear.
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| 650 |
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|a Eigenvalues.
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| 730 |
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|a Synthesis digital library of engineering and computer science.
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| 830 |
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|a Synthesis lectures on mathematics and statistics (Online),
|v # 6.
|x 1938-1751 ;
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| 856 |
4 |
2 |
|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.2200/S00218ED1V01Y200908MAS006
|3 Abstract with links to full text
|