Elementary Linear Algebra, 12/e (AE-Paperback)

Howard Anton , Chris Rorres , Anton Kaul




• New Application Section - A new section on the mathematics of facial recognition has been added to Chapter 10.
• Earlier Linear Transformations - Selected material on linear transformations that was covered later in the previous edition has been moved to Chapter 1 to provide a more complete early introduction to the topic. Specifically, some of the material in Sections 4.10 and 4.11 of the previous edition was extracted to form the new Section 1.9, and the remaining material is now in Section 8.6.
• New Section 4.3 Devoted to Spanning Sets - Section 4.2 of the previous edition dealt with both subspaces and spanning sets. Classroom experience has suggested that too many concepts were being introduced at once, so we have slowed down the pace and split off the material on spanning sets to create a new Section 4.3.
• New Examples - New examples have been added, where needed, to support the exercise sets.
• New Exercises - New exercises have been added with special attention to the expanded early introduction to linear transformations.


• Interrelationships Among Concepts - One of our main pedagogical goals is to convey to the student that linear algebra is not a collection of isolated definitions and techniques, but is rather a cohesive subject with interrelated ideas. One way in which we do this is by using a crescendo of theorems labeled "Equivalent Statements" that continually revisit relationships among systems of equations, matrices, determinants, vectors, linear transformations, and eigenvalues. To get a general sense of this pedagogical technique see Theorems 1.5.3, 1.6.4, 2.3.8, 4.9.8, 5.1.5, 6.4.5, and 8.2.4.
• Smooth Transition to Abstraction - Because the transition from Euclidean spaces to general vector spaces is difficult for many students, considerable effort is devoted to explaining the purpose of abstraction and helping the student .to "visualize" abstract ideas by drawing analogies to familiar geometric ideas.
• Mathematical Precision - We try to be as mathematically precise as is reasonable for students at this level. But we recognize that mathematical precision is something to be learned, so proofs are presented in a patient style that is tailored for beginners:
• Suitability for a Diverse Audience - The text is designed to serve the needs of students in engineering, computer science, biology, physics, business, and economics, as well as those majoring in mathematics.
• Historical Notes - We feel that it is important to give students a sense of mathematical history and to convey that real people created the mathematical theorems and equations they are studying. Accordingly, we have included numerous "Historical Notes" that put various topics in historical perspective.



- 新應用節 - 在第10章中新增了一個關於面部識別數學的節。
- 較早的線性變換 - 將上一版中稍後涵蓋的線性變換相關內容移至第1章,以提供更完整的早期介紹。具體而言,上一版中第4.10節和第4.11節的部分內容被提取出來形成新的第1.9節,其餘內容現在位於第8.6節。
- 新的4.3節專注於生成集 - 上一版的第4.2節涉及子空間和生成集。根據課堂經驗,同時引入太多概念,因此我們放慢了節奏,將生成集的內容分離出來,創建了新的第4.3節。
- 新的例子 - 根據需要添加了新的例子,以支持練習題集。
- 新的練習題 - 添加了新的練習題,特別關注早期線性變換的介紹。


- 概念之間的相互關係 - 我們的主要教學目標之一是向學生傳達線性代數不僅僅是一系列孤立的定義和技巧,而是一門具有相互關聯思想的統一學科。我們通過使用一系列被標記為“等價陳述”的定理來實現這一目標,這些定理不斷重新討論方程組、矩陣、行列式、向量、線性變換和特徵值之間的關係。要對這種教學技巧有一般的了解,請參閱定理1.5.3、1.6.4、2.3.8、4.9.8、5.1.5、6.4.5和8.2.4。
- 平滑過渡到抽象 - 由於從歐幾里得空間到一般向量空間的過渡對許多學生來說很困難,我們花了很多精力解釋抽象的目的,並通過將其與熟悉的幾何概念進行類比來幫助學生“形象化”抽象思想。
- 數學精確性 - 我們試圖在這個水平的學生中保持盡可能的數學精確性。但我們也認識到數學精確性是需要學習的,因此證明以適合初學者的耐心風格呈現。
- 適合多樣化的讀者 - 本書旨在滿足工程、計算機科學、生物學、物理學、商業和經濟學專業的學生的需求,以及主修數學的學生。
- 歷史注解 - 我們認為給學生一種數學歷史的感覺,並傳達真實人們創造了他們正在學習的數學定理和方程的重要性。因此,我們包含了許多將各種主題放在歷史背景下的“歷史注解”。


1 Systems of Linear Equations and Matrices
2 Determinants
3 Euclidean Vector Spaces
4 General Vector Spaces
5 Eigenvalues and Eigenvectors
6 Inner Product Spaces
7 Diagonalization and Quadratic Forms
8 General Linear Transformations
9 Numerical Methods
10 Applications of Linear Algebra
Supplemental Online Topics
• Linear Programming - A Geometric Approach
• Linear Programming - Basic Concepts
• Linear Programming - The Simplex Method
• Vectors in Plane Geometry
• Equilibrium of Rigid Bodies
• The Assignment Problem
• The Determinant Function
• Leontief Economic Models
Appendix A Working with Proofs
Appendix B Complex Numbers
Answers to Exercises 


1 線性方程組和矩陣
2 行列式
3 歐幾里得向量空間
4 一般向量空間
5 特徵值和特徵向量
6 內積空間
7 對角化和二次型
8 一般線性變換
9 數值方法
10 線性代數的應用
- 線性規劃 - 幾何方法
- 線性規劃 - 基本概念
- 線性規劃 - 单纯形法
- 平面幾何中的向量
- 剛體的平衡
- 分配問題
- 行列式函數
- Leontief 經濟模型
附錄 A 證明的處理
附錄 B 複數