A Concise Text on Advanced Linear Algebra (Paperback)
暫譯: 高級線性代數簡明文本(平裝本)

Yang, Yisong

  • 出版商: Cambridge
  • 出版日期: 2015-01-12
  • 售價: $1,200
  • 貴賓價: 9.5$1,140
  • 語言: 英文
  • 頁數: 331
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1107456819
  • ISBN-13: 9781107456815
  • 相關分類: 線性代數 Linear-algebra
  • 下單後立即進貨 (約5~7天)

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商品描述

This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley-Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text.

商品描述(中文翻譯)

這本引人入勝的教科書適合高年級本科生和初學研究生,涵蓋了線性代數的核心主題。作者通過清晰地將概念與應用及其他重要領域(如微分拓撲和量子力學)聯繫起來,來激發讀者的興趣。該書特別強調在適當的地方整合分析的思想。例如,行列式的概念是通過計算向量場的指數來引入的,這導致了代數基本定理的自包含證明,而 Cayley-Hamilton 定理則是通過認識到具有不同特徵值的複數矩陣集合是稠密的事實來建立的。這些材料還附有超過350道以證明為導向的練習題,適合各種背景的學生。書末提供了選擇性的解答,使其適合自學以及作為課程教材使用。