Elementary Linear Algebra (Metric Version - Not available for student purchase in the U.S.) 8th edition

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• Chapter 1: Systems of Linear Equations
  • 1.1: Introduction to Systems of Linear Equations
  • 1.2: Gaussian Elimination and Gauss-Jordan Elimination
  • 1.3: Applications of Systems of Linear Equations
  • 1: Review Exercises
  
  
• Chapter 2: Matrices
  • 2.1: Operations with Matrices
  • 2.2: Properties of Matrix Operations
  • 2.3: The Inverse of a Matrix
  • 2.4: Elementary Matrices
  • 2.5: Markov Chains
  • 2.6: More Applications of Matrix Operations
  • 2: Review Exercises
  
  
• Chapter 3: Determinants
  • 3.1: The Determinant of a Matrix
  • 3.2: Determinants and Elementary Operations
  • 3.3: Properties of Determinants
  • 3.4: Applications of Determinants
  • 3: Review Exercises
  • 3: Cumulative Test
  
  
• Chapter 4: Vector Spaces
  • 4.1: Vectors in Rⁿ
  • 4.2: Vector Spaces
  • 4.3: Subspaces of Vector Spaces
  • 4.4: Spanning Sets and Linear Independence
  • 4.5: Basis and Dimension
  • 4.6: Rank of a Matrix and Systems of Linear Equations
  • 4.7: Coordinates and Change of Basis
  • 4.8: Applications of Vector Spaces
  • 4: Review Exercises
  
  
• Chapter 5: Inner Product Spaces
  • 5.1: Length and Dot Product in Rⁿ
  • 5.2: Inner Product Spaces
  • 5.3: Orthonormal Bases: Gram-Schmidt Process
  • 5.4: Mathematical Models and Least Squares Analysis
  • 5.5: Applications of Inner Product Spaces
  • 5: Review Exercises
  • 5: Cumulative Test
  
  
• Chapter 6: Linear Transformations
  • 6.1: Introduction to Linear Transformations
  • 6.2: The Kernel and Range of a Linear Transformation
  • 6.3: Matrices for Linear Transformations
  • 6.4: Transition Matrices and Similarity
  • 6.5: Applications of Linear Transformations
  • 6: Review Exercises
  
  
• Chapter 7: Eigenvalues and Eigenvectors
  • 7.1: Eigenvalues and Eigenvectors
  • 7.2: Diagonalization
  • 7.3: Symmetric Matrices and Orthogonal Diagonalization
  • 7.4: Applications of Eigenvalues and Eigenvectors
  • 7: Review Exercises
  • 7: Cumulative Test
  
  
• Chapter 8: Complex Vector Spaces (online)
  • 8.1: Complex Numbers
  • 8.2: Conjugates and Division of Complex Numbers
  • 8.3: Polar Form and DeMoivre's Theorem
  • 8.4: Complex Vector Spaces and Inner Products
  • 8.5: Unitary and Hermitian Matrices
  • 8: Review Exercises
  
  
• Chapter 9: Linear Programming (online)
  • 9.1: Systems of Linear Inequalities
  • 9.2: Linear Programming Involving Two Variables
  • 9.3: The Simplex Method: Maximization
  • 9.4: The Simplex Method: Minimization
  • 9.5: The Simplex Method: Mixed Constraints
  • 9: Review Exercises
  
  
• Chapter 10: Numerical Methods (online)
  • 10.1: Gaussian Elimination with Partial Pivoting
  • 10.2: Iterative Methods for Solving Linear Systems
  • 10.3: Power Method for Approximating Eigenvalues
  • 10.4: Applications of Numerical Methods
  • 10: Review Exercises