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LINEAR ALGEBRA AND LTS APPLICATIONSPDF|Epub|txt|kindle电子书版本网盘下载

DAVID C.LAY 著
出版社： ADDISON-WESLEY PUBLISHING COMPANY
ISBN：
出版时间：1993
标注页数：508页
文件大小：74MB
文件页数：525页
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图书目录

1 SYSTEMS OF LINEAR EQUATIONS1

Introductory Example：Linear Models in Economics and Engineering1

1.1 Introduction to Systems of Linear Equations2

1.2 Row Reduction and Echelon Forms13

1.3 Applications of Linear Systems25

Supplementary Exercises34

2 VECTOR AND MATRIX EQUATIONS37

Introductory Example：Nutrition Problems37

2.1 Vectors in R”38

2.2 The Equation Ax＝b48

2.3 Solution Sets of Linear Systems56

2.4 Linear Independence63

2.5 Introduction to Linear Transformations71

2.6 The Matrix of a Linear Transformation79

2.7 Applications to Nutrition and Population Movement85

Supplementary Exercises92

3 MATRIX ALGEBRA95

Introductory Example：Computer Graphics in Automotive Design95

3.1 Matrix Operations96

3.2 The Inverse of a Matrix107

3.3 Characterizations of Invertible Matrices116

3.4 Partitioned Matrices121

3.5 Matrix Factorizations128

3.6 Iterative Solutions of Linear Systems137

3.7 The Leontief Input-Output Model142

3.8 Applications to Computer Graphics148

Supplementary Exercises158

4 DETERMINANTS161

Introductory Example：Determinants in Analytic Geometry161

4.1 Introduction to Determinants162

4.2 Properties of Determinants168

4.3 Cramer’s Rule，Volume，and Linear Transformations176

Supplementary Exercises186

5 VECTOR SPACES189

Introductory Example：Space Flight and Control Systems189

5.1 Vector Spaces and Subspaces190

5.2 Null Spaces，Column Spaces，and Linear Transformations200

5.3 Linearly Independent Sets； Bases211

5.4 Coordinate Systems219

5.5 The Dimension of a Vector Space229

5.6 Rank235

5.7 Change of Basis243

5.8 Applications to Difference Equations248

5.9 Applications to Markov Chains259

Supplementary Exercises269

6 EIGENVALUES AND EIGENVECTORS271

Introductory Example：Dynamical Systems and Spotted Owls271

6.1 Eigenvectors and Eigenvalues273

6.2 The Characteristic Equation280

6.3 Diagonalization288

6.4 Eigenvectors and Linear Transformations296

6.5 Complex Eigenvalues303

6.6 Applications to Dynamical Systems310

6.7 Iterative Estimates for Eigenvalues321

Supplementary Exercises329

7 ORTHOGONALITY AND LEAST-SQUARES331

Introductory Example：Readjusting the North American Datum331

7.1 Inner Product，Length，and Orthogonality333

7.2 Orthogonal Sets342

7.3 Orthogonal Projections352

7.4 The Gram-Schmidt Process359

7.5 Least-Squares Problems366

7.6 Applications to Linear Models376

7.7 Inner Product Spaces384

7.8 Applications of Inner Product Spaces393

Supplementary Exercises401

8 SYMMETRIC MATRICES AND QUADRATIC FORMS403

Introductory Example：Multichannel Image Processing403

8.1 Diagonalization of Symmetric Matrices405

8.2 Quadratic Forms411

8.3 Constrained Optimization419

8.4 The Singular Value Decomposition426

8.5 Applications to Image Processing and Statistics435

Supplementary Exercises444

APPENDICES447

A Uniqueness of the Reduced Echelon Form447

B Complex Numbers449

GLOSSARY455

ANSWERS TO ODD-NUMBERED EXERCISES467