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)

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
Creator
Author
Author
Subject
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
Member of
Is Subseries of
http://library.link/vocab/creatorName
Norman, Christopher
Dewey number
512.25
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
pq8wQ3NMbNQ
Language note
English
LC call number
QA247-QA247.45
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)
Instantiates
Publication
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 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.
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
10.1007/978-1-4471-2730-7
Specific material designation
remote
System control number
  • (CKB)3400000000025507
  • (EBL)3070502
  • (SSID)ssj0000609729
  • (PQKBManifestationID)11434004
  • (PQKBTitleCode)TC0000609729
  • (PQKBWorkID)10623528
  • (PQKB)11464014
  • (DE-He213)978-1-4471-2730-7
  • (MiAaPQ)EBC3070502
  • (EXLCZ)993400000000025507
Label
Finitely Generated Abelian Groups and Similarity of Matrices over a Field, by Christopher Norman, (electronic resource)
Publication
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 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.
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
10.1007/978-1-4471-2730-7
Specific material designation
remote
System control number
  • (CKB)3400000000025507
  • (EBL)3070502
  • (SSID)ssj0000609729
  • (PQKBManifestationID)11434004
  • (PQKBTitleCode)TC0000609729
  • (PQKBWorkID)10623528
  • (PQKB)11464014
  • (DE-He213)978-1-4471-2730-7
  • (MiAaPQ)EBC3070502
  • (EXLCZ)993400000000025507

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