000			04213nam a2200505 i 4500
001			6813086
003			IEEE
005			20200413152855.0
006			m eo d
007			cr cn |||m|||a
008			090909s2009 caua foa 001 0 eng d
020			_a9781608452514 (electronic bk.)
020			_z9781608452507 (pbk.)
024	7		_a10.2200/S00218ED1V01Y200908MAS006 _2doi
035			_a(CaBNVSL)gtp00535641
035			_a(OCoLC)433076263
040			_aCaBNVSL _cCaBNVSL _dCaBNVSL
050		4	_aQA252.5 _b.W455 2009
082	0	4	_a512.24 _222
100	1		_aWeintraub, Steven H.
245	1	0	_aJordan Canonical Form _h[electronic resource] : _btheory and practice / _cSteven H. Weintraub.
260			_aSan Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool Publishers, _cc2009.
300			_a1 electronic text (x, 96 p. : ill.) : _bdigital file.
490	1		_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 6
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat reader.
500			_aPart of: Synthesis digital library of engineering and computer science.
500			_aSeries from website.
500			_aIncludes index.
505	0		_a1. 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.
506	1		_aAbstract freely available; full-text restricted to subscribers or individual document purchasers.
510	0		_aCompendex
510	0		_aINSPEC
510	0		_aGoogle scholar
510	0		_aGoogle book search
520	3		_aJordan 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.
530			_aAlso available in print.
588			_aTitle from PDF t.p. (viewed on September 9, 2009).
650		0	_aJordan algebras.
650		0	_aAlgebras, Linear.
650		0	_aEigenvalues.
730	0		_aSynthesis digital library of engineering and computer science.
830		0	_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 6.
856	4	2	_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=6813086
999			_c561707 _d561707