Linear Algebra and Its Applications, 5/e (IE-Paperback)

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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: The North American Datum and GPS Navigation
   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: Googling 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