Abstract linear algebra

著者

• Curtis, Morton Landers
• Place, Paul

書誌事項

Abstract linear algebra

Morton L. Curtis ; with revisions by Paul Place

（Universitext）

Springer-Verlag, c1990

• : us
• : gw

注記

Includes bibliographical references and index

内容説明・目次

巻冊次

: us ISBN 9780387972633

内容説明

Intended for a first course on the subject, this text begins from scratch and develops the standard topics of Linear Algebra. Its progresses simply towards its ultimate goal, the Theorem of Hurwitz, which argues that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. The book stresses the complete logical development of the subject.

目次

0. Algebraic Preliminaries.- I. Vector Spaces and Linear Maps.- A. Vector Spaces.- B. Linear Maps.- C. Bases, Dimension.- D. Direct Sums, Quotients.- E. Eigenvectors and Eigenvalues (Part i).- F. Dual Spaces.- II. Matrices and Determinants.- A. Matrices.- B. Algebras.- C. Determinants, the Laplace Expansion.- D. Inverses, Systems of Equations.- E. Eigenvalues (Part ii).- III. Rings and Polynomials.- A. Rings.- B. Polynomials.- C. Cayley-Hamilton Theorem.- D. Spectral Theorems.- E. Jordan Form.- IV. Inner Product Spaces.- A. Rn as a Model, Bilinear Forms.- B. Real Inner Product Spaces, Normed Vector Spaces.- C. Complex Inner Product Spaces.- D. Orthogonal and Unitary Groups.- E. Stable Subspaces for Unitary and Orthogonal Groups.- V. Normed Algebras.- A. The Normed Algebras R and C.- B. Some General Results, Quaternions.- C. Alternative and Division Algebras.- D. Cayley-Dickson Process, Hurwitz Theorem.

巻冊次

: gw ISBN 9783540972631

内容説明

Beginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. In presenting this material at an elementary level, the book stresses the complete logical development of the subject and should be a suitable reference for mathematicians in general.

目次

Contents: Algebraic Preliminaries.- Vector Spaces and Linear Maps.- Matrices and Determinants.- Rings and Polynomials.- Inner Product Spaces.- Normed Algebras.- Bibliography.- Index.

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詳細情報

• NII書誌ID(NCID): BA10610486
• ISBN:
  • 0387972633
  • 3540972633
• LCCN: 90033058
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: x, 168 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA184
  • DC20 : 512/.5
  • NDC8 : 411.3
• 件名:
  • LCSH : Algebras, Linear
• 親書誌ID:
  • BA00021004