David C.Lay：是一位教育家，發(fā)表過30余篇關(guān)于函數(shù)分析和線性代數(shù)的研究論文。他還是由美國國家科學(xué)基金會(huì)資助的線性代數(shù)課程研究小組的創(chuàng)始人。Lay參與編寫了包括“Introduction to Functional Analysis”、“Calculus and Its Applications”和“Linear Algebra Gems-Assets for Undergraduate Mathematics”在內(nèi)的幾本書。
圖書目錄
Chapter 1 Linear Equations in Linear Algebra 1 INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 1 1.1 Systems of Linear Equations 2 1.2 Row Reduction and Echelon Forms 14 1.3 Vector Equations 28 1.4 The Matrix Equation Ax =b 40 1.5 Solution Sets of Linear Systems 50 1.6 Applications of Linear Systems 57 1.7 Linear Independence 65 1.8 Introduction to Linear Transformations 73 1.9 The Matrix of a Linear Transformation 82 1.10 Linear Models in Business, Science, and Engineering 92 Supplementary Exercises. 102 Chapter 2 Matrix Alflebra 105 INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 105 2.1 Matrix Operations 107 2.2 The Inverse of a Matrix 118 2.3 Characterizations of Invertible Matrices 128 2.4 Partitioned Matrices 134 2.5 Matrix Factorizations 142 2.6 The Leontief Input-Output Model 152 2.7 Applications to Computer Graphics 158 2.8 Subspaces of R 167 2.9 Dimension and Rank 176 Supplementary Exercises 183 Chapter 3 Determinants 185 INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry 185 3.1 Introduction to Determinants 186 3.2 Properties of Determinants 192 3.3 Cramer's Rule, Volume, and Linear Transformations 201 Supplementary Exercises 211 Chapter 4 Vector Spaces 215 INTRODUCTORY EXAMPLE: Space Flight and Control Systems 215 4.1 Vector Spaces and Subspaces 216 4.2 Null Spaces, Column Spaces, and Linear Transformations 226 4.3 Linearly Independent Sets; Bases 237 4.4 Coordinate Systems 246 4.5 The Dimension of a Vector Space 256 4.6 Rank 262 4.7 Change of Basis 271 4.8 Applications to Difference Equations 277 4.9 Applications to Markov Chains 288 Supplementary Exercises 299 Chapter 5 Eigenvalues and Eigenvectors 301 INTRODUCTORY EXAMPLE' Dynamical Systems and Spotted Owls 301 5.1 Eigenvectors and Eigenvalues 302 512 The Characteristic Equation 310 5.3 Diagonalization 319 5.4 Eigenvectors and Linear Transformations 327 5.5 Complex Eigenvaiues 335 5.6 Discrete Dynamical Systems 342 5.7 Applications to Differential Equations 353 5.8 terative Estimates for Eigenvalues 363 Supplementary Exercises 370 Chapter 6 Orthogonality and Least Squares 373 INSTRODUCTORY EXAMPLE: Readjusting the North American Datum 373 6.1 Inner Product, Length, and Orthogonality 375 6.2 Orthogonal Sets 384 6.3 Orthogonal Projections 394 6.4 The Gram-Schmidt Process 402 6.5 Least-Squares Problems 409 6.6 Applications to Linear Models 419 6.7 Inner Product Spaces 427 6.8 Applications of Inner Product Spaces 436 Supplementary Exercises 444 Chapter 7 Symmetric Matrices and Quadratic Forms 447 INSTRODUCTORY EXAMPLE: Multichannel Image Processing 447 7.1 Diagonalization of Symmetric Matrices 449 7.2 Quadratic Forms 455 7.3 Constrained Optimization 463 7.4 The Singular Value Decomposition 471 7.5 Applications to Image Processing and Statistics 482 Supplementary Exercises 491 Appendixes A Uniqueness of the Reduced Echelon Form A1 B Complex Numbers A3 Glossary A9 Answers to Odd-Numbered Exercises A19 Index II
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