线性代数 第4版 Linear AlgebraAn Introductory Approach 英文原版 Charles WCurtis

基本信息

Format Hardback | 350 pages

Dimensions 155 x 235 x 25.4mm | 1,520g

Publication date 19 Aug 1999

Publisher Springer-Verlag New York Inc.

Language English

Edition Revised

Edition Statement 4th ed. 1984. Corr. 7th printing 1999

Illustrations note X, 350 p.

ISBN10 0387909923

ISBN13 9780387909929

书籍简介

为线性代数高分课程设计的第四版修订和更新包括域上向量空间、行列式、单线性变换理论和内积空间的基本结果。虽然它不以较早的课程为前提，但讨论中涉及了线性代数和微积分之间的许多联系。一个特点是包含了专门用于线性代数应用的部分，这些部分可以是课程的一部分，也可以用于独立学习，本版的新内容是矩阵理论中的分析方法部分，适用于马尔可夫链在概率论中。包括所有主要定理的证明，并与解决数值问题的方法同等地提出。几乎每个部分都集成了工作示例，以带出定理的含义，并说明解决问题的技巧。许多数值练习利用了所有的想法，并培养了计算技能，而理论性质的练习则为学生提供了自己发现的机会。

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.

“这本书是对线性代数文献的重要补充。很高兴将它用于为认真（和有才华的）学生设计的一个学期或两个季度的课程。这本书值得对 当前这一代数学学生就像 45 年前的 Halmos 与这位评论家那一代的有限维向量空间一样。”-MATHEMATICAL REVIEWS

"This book is an important addition to the literature of linear algebra. It would be a pleasure to use it for a one-semester or two-quarter course intended for serious (and talented) students. This book deserves to be as influential with the current generation of mathematics students as was Halmos' Finite-Dimensional Vector Spaces with this reviewer's generation, 45 years ago."-MATHEMATICAL REVIEWS

目录

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.

作者简介

查尔斯·惠特尔西·柯蒂斯（Charles Whittlesey Curtis，1926 年 10 月 13 日出生）是一位数学家和数学历史学家，以其在有限群论和表示论方面的工作而闻名。 他是俄勒冈大学的退休数学教授。

Charles Whittlesey Curtis (born October 13, 1926) is a mathematician and historian of mathematics, known for his work in finite group theory and representation theory. He is a retired professor of mathematics at the University of Oregon.