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线性代数及其应用 英文版【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

线性代数及其应用 英文版
  • （美）DavidC.Lay著 著
  • 出版社： 北京：电子工业出版社
  • ISBN：9787121113956
  • 出版时间：2010
  • 标注页数：560页
  • 文件大小：113MB
  • 文件页数：577页
  • 主题词：线性代数－高等学校－教材－英文

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图书目录

CHAPTER 1　Linear Equations in Linear Algebra1

INTRODUCTORY EXAMPLE:Linear Models in Economics and Engineering1

1.1 Systems of Linear Equations2

1.2 Row Reduction and Echelon Forms14

1.3 Vector Equations28

1.4　The Matrix Equation Ax=b40

1.5 Solution Sets of Linear Systems50

1.6 Applications of Linear Systems57

1.7　Linear Independence65

1.8 Introduction to Linear Transformations73

1.9　The Matrix of a Linear Transformation82

1.10　Linear Models in Business,Science,and Engineering92

Supplementary Exercises102

CHAPTER 2 Matrix Algebra105

INTRODUCTORY EXAMPLE:Computer Models in Aircraft Design105

2.1 Matrix Operations107

2.2　The Inverse of a Matrix118

2.3 Characterizations of Invertible Matrices128

2.4　Partitioned Matrices134

2.5 Matrix Factorizations142

2.6　The Leontief Input-Output Model152

2.7 Applications to Computer Graphics158

2.8 Subspaces of Rn167

2.9　Dimension and Rank176

Supplementary Exercises183

CHAPTER 3　Determinants185

INTRODUCTORY EXAMPLE:Determinants in Analytic Geometry185

3.1 Introduction to Determinants186

3.2　Properties of Determinants192

3.3 Cramer's Rule,Volume,and Linear Transformations201

Supplementary Exercises211

CHAPTER 4　Vector Spaces215

INTRODUCTORY EXAMPLE:Space Flight and Control Systems215

4.1 Vector Spaces and Subspaces216

4.2 Null Spaces,Column Spaces,and Linear Transformations226

4.3　Linearly Independent Sets;Bases237

4.4 Coordinate Systems246

4.5　The Dimension of a Vector Space256

4.6 Rank262

4.7 Change of Basis271

4.8 Applications to Difference Equations277

4.9 Applications to Markov Chains288

Supplementary Exercises299

CHAPTER 5　Eigenvalues and Eigenvectors301

INTRODUCTORY EXAMPLE:Dynamical Systems and Spotted Owls301

5.1 Eigenvectors and Eigenvalues302

5.2　The Characteristic Equation310

5.3　Diagonalization319

5.4 Eigenvectors and Linear Transformations327

5.5 Complex Eigenvalues335

5.6　Discrete Dynamical Systems342

5.7 Applications to Differential Equations353

5.8 Iterative Estimates for Eigenvalues363

Supplementary Exercises370

CHAPTER 6　Orthogonality and Least Squares373

INTRODUCTORY EXAMPLE:Readjusting the North American Datum373

6.1 Inner Product,Length,and Orthogonality375

6.2 Orthogonal Sets384

6.3 Orthogonal Projections394

6.4　The Gram-Schmidt Process402

6.5　Least-Squares Problems409

6.6 Applications to Linear Models419

6.7 Inner Product Spaces427

6.8 Applications of Inner Product Spaces436

Supplementary Exercises444

CHAPTER 7　SVmmetric Matrices and Quadratic Forms447

INTRODUCTORY EXAMPLE:Multichannel Image Processing447

7.1　Diagonalization of Symmetric Matrices449

7.2 Quadratic Forms455

7.3 Constrained Optimization463

7.4　The Singular Value Decomposition471

7.5 Applications to Image Processing and Statistics482

Supplementary Exercises491

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