Algebras of linear transformations
Author(s)
Bibliographic Information
Algebras of linear transformations
(Universitext)
Springer, c2001
Available at 28 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. 233-234) and index
Description and Table of Contents
Description
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.
Table of Contents
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.
by "Nielsen BookData"