دانلود کتاب Linear Algebra and Its Applications, Global Edition

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Cover Title Page Copyright Dedication About the Authors Contents Applications Index Preface Get the most out of MyLab Math Resources for Success A Note to Students Chapter 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 Projects Supplementary Exercises Chapter 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 Projects Supplementary Exercises Chapter 3: Determinants Introductory Example: Weighing Diamonds 3.1 Introduction to Determinants 3.2 Properties of Determinants 3.3 Cramer’s Rule, Volume, and Linear Transformations Projects Supplementary Exercises Chapter 4: Vector Spaces Introductory Example: Discrete-Time Signals and Digital Signal Processing 4.1 Vector Spaces and Subspaces 4.2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations 4.3 Linearly Independent Sets; Bases 4.4 Coordinate Systems 4.5 The Dimension of a Vector Space 4.6 Change of Basis 4.7 Digital Signal Processing 4.8 Applications to Difference Equations Projects Supplementary Exercises Chapter 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 5.9 Applications to Markov Chains Projects Supplementary Exercises Chapter 6: Orthogonality and Least Squares Introductory Example: Artificial Intelligence and Machine Learning 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 Machine Learning and Linear Models 6.7 Inner Product Spaces 6.8 Applications of Inner Product Spaces Projects Supplementary Exercises Chapter 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 Projects Supplementary Exercises Chapter 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 Project Supplementary Exercises Chapter 9: Optimization Introductory Example: The Berlin Airlift 9.1 Matrix Games 9.2 Linear Programming Geometric Method 9.3 Linear Programming Simplex Method 9.4 Duality Project Supplementary Exercises Chapter 10: Finite-State Markov Chains 10.1 Introduction and Examples 10.2 The Steady-State Vector and Google’s PageRank 10.3 Communication Classes 10.4 Classification of States and Periodicity 10.5 The Fundamental Matrix 10.6 Markov Chains and Baseball Statistics Appendix 1: Proof of Theorem 1 Appendix 2: Probability Answers to Selected Exercises Appendixes Appendix A: Uniqueness of the Reduced Echelon Form Appendix B: Complex Numbers Credits Glossary Answers to Odd-Numbered Exercises Index A B C D E F G H I J K L M N O P Q R S T U V W Z Advice on Reading Linear Algebra