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This book studies algebras and linear transformations acting on finite-dimensional vector spaces over arbitrary fields. It is written for readers who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for readers to gain a firm understanding of the basic theory of finite-dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Contenuti
1. Linear Algebra.- 1.1 Vector Spaces and Duality.- 1.2 Direct Sums and Quotients.- 1.3 Inner-Product Spaces.- 1.4 The Spectral Theorem.- 1.5 Fields and Field Extensions.- 1.6 Existence of Bases for Infinite-Dimensional Spaces.- 1.7 Notes.- 1.8 Exercises.- 2. Algebras.- 2.1 Algebrai c Structures.- 2.2 Algebras with a Prescribed Basis.- 2.3 Algebras of Linear Transformations.- 2.4 Inversion and Spectra.- 2.5 Division Algebras and Other Simple Algebras.- 2.6 Notes.- 2.7 Exercises.- 3. Invariant Subspaces.- 3.1 The Invariant-Subspace Lattice.- 3.2 Idempotents and Projections.- 3.3 Existence of Invariant Subspaces.- 3.4 Representations and Left Ideals.- 3.5 Functional Calculus and Polar Decomposition.- 3.6 Notes.- 3.7 Exercises.- 4. Semisimple Algebras.- 4.1 Nilpotent Algebras and the Nil Radical.- 4.2 Structure of Semisimple Algebras.- 4.3 Structure of Simple Algebras.- 4.4 Isomorphism Classes of Semisimple Algebras.- 4.5 Notes.- 4.6 Exercises.- 5. Operator Algebras.- 5.1 Von Neumann Algebras.- 5.2 Real and Complex Involutive Algebras.- 5.3 Representation of Operator Algebras.- 5.4 Wedderburn Theorems for Operator Algebras.- 5.5 C*-Algebras.- 5.5 Notes.- 5.7 Exercises.- 6. Tensor Products.- 6.1 Free Vector Spaces.- 6.2 Tensor Products of Vector Spaces.- 6.3 Tensor Products of Algebras.- 6.4 Tensor Products of Operator Algebras.- 6.5 Notes.- 6.6 Exercises.- References.
Product Description
Book by Farenick Douglas R
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- EditoreSpringer Verlag
- Data di pubblicazione2000
- ISBN 10 0387950621
- ISBN 13 9780387950624
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine238
- Contatto del produttorenon disponibile
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Algebras of Linear Transformations
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Hardcover. Condizione: ex library-good. xiv, 238 p. 25 cm. Ex library with labels on spine and front cover, ink stamps on rear pastedown, top edge and title. Spine crease, a bit of soiling to outside. Corners and spine ends bumped. Codice articolo 148268
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book studies algebras and linear transformations acting on finite-dimensional vector spaces over arbitrary fields. It is written for readers who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example . Codice articolo 5912313
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Algebras of Linear Transformations (Universitext)
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Condizione: Fine. First edition, first printing, 253 pp., Hardcover, some FAINT wear to front cover else LIKE NEW. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Codice articolo ZB1325293
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book studies algebras and linear transformations acting on finite -dimensional vector spaces over arbitrary fields. It is written for students who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for students to gain a firm understanding of the basic theory of finite- dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics. As such, the level of exposition is suitable for senior undergraduate students. 260 pp. Englisch. Codice articolo 9780387950624
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Algebras of Linear Transformations
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ISBN 10: 0387950621
ISBN 13: 9780387950624
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Buch. Condizione: Neu. Neuware -The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans formations in one guise or another are standard features of various parts of modern mathematics. These include well-entrenched fields such as repre sentation theory, as well as newer ones such as quantum groups. Second, a study ofthe elementary theory offinite-dimensional algebras is particularly useful in motivating and casting light upon more sophisticated topics such as module theory and operator algebras. Indeed, the reader who acquires a good understanding of the basic theory of algebras is wellpositioned to ap preciate results in operator algebras, representation theory, and ring theory. In return for their efforts, readers are rewarded by the results themselves, several of which are fundamental theorems of striking elegance.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 260 pp. Englisch. Codice articolo 9780387950624
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Algebras of Linear Transformations
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans formations in one guise or another are standard features of various parts of modern mathematics. These include well-entrenched fields such as repre sentation theory, as well as newer ones such as quantum groups. Second, a study ofthe elementary theory offinite-dimensional algebras is particularly useful in motivating and casting light upon more sophisticated topics such as module theory and operator algebras. Indeed, the reader who acquires a good understanding of the basic theory of algebras is wellpositioned to ap preciate results in operator algebras, representation theory, and ring theory. In return for their efforts, readers are rewarded by the results themselves, several of which are fundamental theorems of striking elegance. Codice articolo 9780387950624
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Algebras of Linear Transformations
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ISBN 13: 9780387950624
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