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001			287069
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007			cr nn 008mamaa
008			150903s2012 xxk| o |||| 0|eng d
020			_a9781447127307 _99781447127307
024	7		_a10.1007/9781447127307 _2doi
035			_avtls000339613
039		9	_a201509030318 _bVLOAD _c201404300402 _dVLOAD _y201402060939 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA161.A-161.Z
100	1		_aNorman, Christopher. _eautor _9316084
245	1	0	_aFinitely Generated Abelian Groups and Similarity of Matrices over a Field / _cby Christopher Norman.
264		1	_aLondon : _bSpringer London, _c2012.
300			_axii, 381 páginas _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aSpringer Undergraduate Mathematics Series, _x1615-2085
500			_aSpringer eBooks
505	0		_aPart 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form -- Basic Theory of Additive Abelian Groups -- Decomposition of Finitely Generated  Z-Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x] and Matrices over F[x]- F[x] Modules: Similarity of t xt Matrices over a Field F -- Canonical Forms and Similarity Classes of Square Matrices over a Field.        .
520			_aAt first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common.  However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases.  Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical.  The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal.  Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with the elementary properties of rings and fields.  Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions.  The early chapters form an ideal second course in algebra for second and third year undergraduates.  The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students.  The book is a bridge between linear and abstract algebra.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9781447127291
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-1-4471-2730-7 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c287069 _d287069