Finitely generated abelian groups and similarity of matrices over a field
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...
Enregistré dans:
| 主要作者: | |
|---|---|
| 格式: | Livre numérique |
| 語言: | Anglais |
| 出版: |
London :
Springer London
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2012. |
| 叢編: | Springer Undergraduate Mathematics Series
|
| 主題: | |
| 在線閱讀: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 提示: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Finitely Generated Abelian Groups and Similarity of Matrices over a Field, Texte imprimé, 9781447127291 |
| LEADER | 04254nam a22003737a 4500 | ||
|---|---|---|---|
| 001 | 973994 | ||
| 008 | 120309q2000 xx ||| |||| 00| 0 eng d | ||
| 009 | PPN159081548 | ||
| 020 | |a 9781447127307 |z 9781447127307 | ||
| 020 | |a 9781447127307 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.3 | ||
| 100 | 1 | |a Norman, Christopher. | |
| 245 | 1 | 0 | |a Finitely generated abelian groups and similarity of matrices over a field |c by Christopher Norman. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Undergraduate Mathematics Series |x 2197-4144 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Théorie des champs (physique) | ||
| 650 | |a Groupes abéliens | ||
| 650 | |a Polynômes matriciels | ||
| 776 | 0 | |t Finitely Generated Abelian Groups and Similarity of Matrices over a Field |b Texte imprimé |z 9781447127291 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-1-4471-2730-7 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-TDV0206G-3 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750605421 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-1-4471-2730-7 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:753965399 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-1-4471-2730-7 |z Accès INSA CVL | |
| 997 | |0 973994 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||