Linear Algebra and Its Applications, 5/e (IE-Paperback)

全新的，國際版/全球版，主要內容基本相同，以優惠價格出售。

1. Linear Equations in Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering
Supplementary Exercises

2. Matrix Algebra
Introductory Example: Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input–Output Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank
Supplementary Exercises

3. Determinants
Introductory Example: Random Paths and Distortion
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer’s Rule, Volume, and Linear Transformations
Supplementary Exercises

4. Vector Spaces
Introductory Example: Space Flight and Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercises

5. Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
Supplementary Exercises

6. Orthogonality and Least Squares
Introductory Example: The North American Datum and GPS Navigation
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram–Schmidt Process
6.5 Least-Squares Problems
6.6 Applications to Linear Models
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces
Supplementary Exercises
 
7. Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
Supplementary Exercises

8. The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces

9. Optimization (Online Only)
Introductory Example: The Berlin Airlift
9.1 Matrix Games
9.2 Linear Programming—Geometric Method
9.3 Linear Programming—Simplex Method
9.4 Duality

10. Finite-State Markov Chains (Online Only)
Introductory Example: Googling Markov Chains
10.1 Introduction and Examples
10.2 The Steady-State Vector and Google's PageRank
10.3 Finite-State Markov Chains
10.4 Classification of States and Periodicity
10.5 The Fundamental Matrix
10.6 Markov Chains and Baseball Statistics

1. 線性代數中的線性方程組
- 入門示例：經濟學和工程學中的線性模型
- 1.1 線性方程組
- 1.2 行簡化和梯形形式
- 1.3 向量方程
- 1.4 矩陣方程 Ax = b
- 1.5 線性系統的解集
- 1.6 線性系統的應用
- 1.7 線性獨立性
- 1.8 線性變換入門
- 1.9 線性變換的矩陣
- 1.10 商業、科學和工程中的線性模型
- 附加練習

2. 矩陣代數
- 入門示例：飛機設計中的計算機模型
- 2.1 矩陣運算
- 2.2 矩陣的逆
- 2.3 可逆矩陣的特徵
- 2.4 分割矩陣
- 2.5 矩陣分解
- 2.6 Leontief 輸入-輸出模型
- 2.7 運用於計算機圖形學
- 2.8 Rn 的子空間
- 2.9 維度和秩
- 附加練習

3. 行列式
- 入門示例：隨機路徑和扭曲
- 3.1 行列式入門
- 3.2 行列式的性質
- 3.3 Cramer 法則、體積和線性變換
- 附加練習

4. 向量空間
- 入門示例：太空飛行和控制系統
- 4.1 向量空間和子空間
- 4.2 零空間、列空間和線性變換
- 4.3 線性獨立集合；基底
- 4.4 座標系統
- 4.5 向量空間的維度
- 4.6 秩
- 4.7 基底的變換
- 4.8 運用於差分方程
- 4.9 運用於馬可夫鏈
- 附加練習

5. 特徵值和特徵向量
- 入門示例：動態系統和斑點貓頭鷹
- 5.1 特徵向量和特徵值
- 5.2 特徵方程
- 5.3 對角化
- 5.4 特徵向量和線性變換
- 5.5 複數特徵值
- 5.6 離散動態系統
- 5.7 運用於微分方程
- 5.8 特徵值的迭代估計
- 附加練習

6. 正交性和最小二乘法
- 入門示例：北美大地基準和 GPS 導航
- 6.1 內積、長度和正交性
- 6.2 正交集合
- 6.3 正交投影
- 6.4 Gram-Schmidt 過程
- 6.5 最小二乘問題
- 6.6 線性模型的應用
- 6.7 內積空間
- 6.8 內積空間的應用
- 附加練習

7. 對稱矩陣和二次型
- 入門示例：多通道圖像處理
- 7.1 對稱矩陣的對角化
- 7.2 二次型
- 7.3 有限制的最佳化
- 7.4 奇異值分解
- 7.5 運用於圖像處理和統計學
- 附加練習

8. 向量空間的幾何
- 入門示例：柏拉圖立體
- 8.1 仿射組合
- 8.2 仿射獨立性
- 8.3 凸組合
- 8.4 超平面
- 8.5 多面體
- 8.6 曲線和曲面

9. 最佳化（僅線上提供）
- 入門示例：柏林空運
- 9.1 矩陣遊戲
- 9.2 線性規劃-幾何方法
- 9.3 線性規劃-單純形法
- 9.4 對偶性

10. 有限狀態馬可夫鏈（僅線上提供）
- 入門示例：Google 的馬可夫鏈
- 10.1 簡介和示例
- 10.2 穩態向量和 Google 的 PageRank
- 10.3 有限狀態馬可夫鏈
- 10.4 狀態分類和週期性
- 10.5 基本矩陣
- 10.6 運用於棒球統計學