Linear Algebra: A Modern Introduction 4th edition

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• Chapter 1: Vectors
  • 1.0: Introduction: The Racetrack Game
  • 1.1: The Geometry and Algebra of Vectors
  • 1.2: Length and Angle: The Dot Product
  • 1.3: Lines and Planes
  • 1.4: Applications
  • 1: Chapter Review
  
  
• Chapter 2: Systems of Linear Equations
  • 2.0: Introduction: Triviality
  • 2.1: Introduction to Systems of Linear Equations
  • 2.2: Direct Methods for Solving Linear Systems
  • 2.3: Spanning Sets and Linear Independence
  • 2.4: Applications
  • 2.5: Iterative Methods for Solving Linear Systems
  • 2: Chapter Review
  
  
• Chapter 3: Matrices
  • 3.0: Introduction: Matrices in Action
  • 3.1: Matrix Operations
  • 3.2: Matrix Algebra
  • 3.3: The Inverse of a Matrix
  • 3.4: The LU Factorization
  • 3.5: Subspaces, Basis, Dimension, and Rank
  • 3.6: Introduction to Linear Transformations
  • 3.7: Applications
  • 3: Chapter Review
  
  
• Chapter 4: Eigenvalues and Eigenvectors
  • 4.0: Introduction: A Dynamical System on Graphs
  • 4.1: Introduction to Eigenvalues and Eigenvectors
  • 4.2: Determinants
  • 4.3: Eigenvalues and Eigenvectors of n × n Matrices
  • 4.4: Similarity and Diagonalization
  • 4.5: Iterative Methods for Computing Eigenvalues
  • 4.6: Applications and the Perron-Frobenius Theorem
  • 4: Chapter Review
  
  
• Chapter 5: Orthogonality
  • 5.0: Introduction: Shadows on a Wall
  • 5.1: Orthogonality in ℜⁿ
  • 5.2: Orthogonal Complements and Orthogonal Projections
  • 5.3: The Gram-Schmidt Process and the QR Factorization
  • 5.4: Orthogonal Diagonalization of Symmetric Matrices
  • 5.5: Applications
  • 5: Chapter Review
  
  
• Chapter 6: Vector Spaces
  • 6.0: Introduction: Fibonacci in (Vector) Space
  • 6.1: Vector Spaces and Subspaces
  • 6.2: Linear Independence, Basis, and Dimension
  • 6.3: Change of Basis
  • 6.4: Linear Transformations
  • 6.5: The Kernel and Range of a Linear Transformation
  • 6.6: The Matrix of a Linear Transformation
  • 6.7: Applications
  • 6: Chapter Review
  
  
• Chapter 7: Distance and Approximation
  • 7.0: Introduction: Taxicab Geometry
  • 7.1: Inner Product Spaces
  • 7.2: Norms and Distance Functions
  • 7.3: Least Squares Approximation
  • 7.4: The Singular Value Decomposition
  • 7.5: Applications
  • 7: Chapter Review
  
  
• Chapter 8: Codes (Online only)
  • 8.1: Code Vectors
  • 8.2: Error-Correcting
  • 8.3: Dual Codes
  • 8.4: Linear Codes
  • 8.5: The Minimum Distance of a Code
  
  
• Chapter A: Appendices
  • A.A: Mathematical Notation and Methods of Proof
  • A.B: Mathematical Induction
  • A.C: Complex Numbers
  • A.D: Polynomials
  • A.E: Technology Bytes (Online only)