000			03267nam a22003615i 4500
001			387515
003			ES-MaUEC
005			20230102122337.0
007			cr nn 008mamaa
008			220601s2009 sz | s |||| 0|eng d
020			_a9783031023989
024	7		_a10.1007/978-3-031-02398-9 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC
050		4	_aQA252.5 _b2009
100	1		_aWeintraub, Steven _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aJordan Canonical Form _bTheory and Practice _cby Steven Weintraub.
250			_a1st edition 2009
264		1	_aCham _bSpringer International Publishing _c2009
300			_a1 recurso en línea (XI, 96 páginas) _b
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Mathematics & Statistics _x1938-1751
505	0		_aJordan Canonical Form -- Solving Systems of Linear Differential Equations -- Background Results: Bases, Coordinates, and Matrices -- Properties of the Complex Exponential.
520			_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 labeled eigenstructure picture (ℓESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader. Table of Contents: Fundamentals on Vector Spaces and Linear Transformations / The Structure of a Linear Transformation / An Algorithm for Jordan Canonical Form and Jordan Basis.
776	0	8	_iPrinted edition: _z9783031012709
776	0	8	_iPrinted edition: _z9783031035265
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02398-9 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
988			_aSynthesis Collection of Technology_2009
999			_c387515 _d387515