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首页 Linear Algebra and Its Applicationstxt,chm,pdf,epub,mobi下载作者:David C. Lay 出版社: Pearson 出版年: 2011-1-20 页数: 576 定价: USD 207.60 装帧: Hardcover ISBN: 9780321385178 内容简介 · · · · · ·Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easil... 作者简介 · · · · · ·David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of ... 目录 · · · · · ·1. Linear Equations in Linear AlgebraIntroductory 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. 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: Readjusting the North American Datum 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: Google and 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 Appendices A. Uniqueness of the Reduced Echelon Form B. Complex Numbers · · · · · · () |
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作者： 泡芙李李
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还没看 不错
以前就看过的书
好评！有一本神奇的新书！