Linear algebra : an introductory approach
著者
書誌事項
Linear algebra : an introductory approach
（Undergraduate texts in mathematics）
Springer-Verlag, c1984
- : us
- : gw
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注記
Bibliography: p. 315-316
Includes index
内容説明・目次
- 巻冊次
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: us ISBN 9780387909929
内容説明
This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.
目次
Preface. 1: Introduction to Linear Algebra. 2: Vector Spaces and Systems of Linear Equations. 3: Linear Transformation and Matrices. 4: Vector Spaces with an Inner Product. 5: Determinants. 6: Polynomials and Complex Numbers. 7: The Theory of a Single Linear Transformation. 8: Dual Vector Spaces and Multilinear Algebra. 9: Orthogonal and Unitary Transformations. 10: Some Applications of Linear Algebra. Bibliography. Solutions of Selected Exercises. Symbols (Including Greek Letters). Index.
- 巻冊次
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: gw ISBN 9783540909927
内容説明
This book is an introduction to linear algebra, designed as a textbook for upper-division courses. It includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. Proofs of all the main theorems are given, with numerical examples, exercises, and applications to geometry, group theory, and differential equations.
目次
Introduction to Linear Algebra.- Vector Spaces and Systems of Linear Equations.- Linear Transformations and Matrices.- Vector Spaces with an Inner Product.- Determinants.- Polynomials and Complex Numbers.- The Theory of a Single Linear Transformation.- Dual Vector Spaces and Multilinear Algebra.- Orthogonal and Unitary Transformations.- Some Applications of Linear Algebra.- Bibliography (with Notes).- Solutions of Selected Exercises.- Symbols (Including Greek Letters).- Index.
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