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The Resource Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource)
Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource)
Resource Information
The item Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 At 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
 Language

 eng
 eng
 Edition
 1st ed. 2012.
 Extent
 1 online resource (388 p.)
 Note
 Includes index
 Contents

 Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form
 Basic Theory of Additive Abelian Groups
 Decomposition of Finitely Generated ZModules. 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.
 Isbn
 9781447127307
 Label
 Finitely Generated Abelian Groups and Similarity of Matrices over a Field
 Title
 Finitely Generated Abelian Groups and Similarity of Matrices over a Field
 Statement of responsibility
 by Christopher Norman
 Language

 eng
 eng
 Summary
 At 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
 http://library.link/vocab/creatorName
 Norman, Christopher
 Dewey number
 512.25
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 pq8wQ3NMbNQ
 Language note
 English
 LC call number
 QA247QA247.45
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer undergraduate mathematics series,
 Springer Undergraduate Mathematics Series,
 http://library.link/vocab/subjectName

 Field theory (Physics)
 Group theory
 Matrix theory
 Algorithms
 Field Theory and Polynomials
 Group Theory and Generalizations
 Linear and Multilinear Algebras, Matrix Theory
 Algorithms
 Label
 Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource)
 Note
 Includes index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form  Basic Theory of Additive Abelian Groups  Decomposition of Finitely Generated ZModules. 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.
 Dimensions
 unknown
 Edition
 1st ed. 2012.
 Extent
 1 online resource (388 p.)
 Form of item
 online
 Isbn
 9781447127307
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781447127307
 Specific material designation
 remote
 System control number

 (CKB)3400000000025507
 (EBL)3070502
 (SSID)ssj0000609729
 (PQKBManifestationID)11434004
 (PQKBTitleCode)TC0000609729
 (PQKBWorkID)10623528
 (PQKB)11464014
 (DEHe213)9781447127307
 (MiAaPQ)EBC3070502
 (EXLCZ)993400000000025507
 Label
 Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource)
 Note
 Includes index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents
 Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form  Basic Theory of Additive Abelian Groups  Decomposition of Finitely Generated ZModules. 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.
 Dimensions
 unknown
 Edition
 1st ed. 2012.
 Extent
 1 online resource (388 p.)
 Form of item
 online
 Isbn
 9781447127307
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781447127307
 Specific material designation
 remote
 System control number

 (CKB)3400000000025507
 (EBL)3070502
 (SSID)ssj0000609729
 (PQKBManifestationID)11434004
 (PQKBTitleCode)TC0000609729
 (PQKBWorkID)10623528
 (PQKB)11464014
 (DEHe213)9781447127307
 (MiAaPQ)EBC3070502
 (EXLCZ)993400000000025507
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