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Lay's Linear Algebra

Study guide for Linear Algebra and Its Applications (David C. Lay, 6th edition)

A study guide for Linear Algebra and Its Applications by David Lay, 6th edition, covering every section with practice problems and quizzes.

Independent study guide. Not affiliated with or endorsed by Pearson.

Chapter 1: Linear Equations in Linear Algebra

  1. 1.1Systems of linear equations
  2. 1.2Row reduction and echelon forms
  3. 1.3Vector equations
  4. 1.4The matrix equation Ax = b
  5. 1.5Solution sets of linear systems
  6. 1.6Applications of linear systems
  7. 1.7Linear independence
  8. 1.8Introduction to linear transformations
  9. 1.9The matrix of a linear transformation
  10. 1.10Linear models in business, science, and engineering

Chapter 2: Matrix Algebra

  1. 2.1Matrix operations
  2. 2.2The inverse of a matrix
  3. 2.3Characterizations of invertible matrices
  4. 2.4Partitioned matrices
  5. 2.5Matrix factorizations
  6. 2.6The Leontief input-output model
  7. 2.7Applications to computer graphics
  8. 2.8Subspaces of R^n
  9. 2.9Dimension and rank

Chapter 3: Determinants

  1. 3.1Introduction to determinants
  2. 3.2Properties of determinants
  3. 3.3Cramer's rule, volume, and linear transformations

Chapter 4: Vector Spaces

  1. 4.1Vector spaces and subspaces
  2. 4.2Null spaces, column spaces, and linear transformations
  3. 4.3Linearly independent sets and bases
  4. 4.4Coordinate systems
  5. 4.5The dimension of a vector space
  6. 4.6Change of basis
  7. 4.7Digital signal processing
  8. 4.8Applications to difference equations

Chapter 5: Eigenvalues and Eigenvectors

  1. 5.1Eigenvectors and eigenvalues
  2. 5.2The characteristic equation
  3. 5.3Diagonalization
  4. 5.4Eigenvectors and linear transformations
  5. 5.5Complex eigenvalues
  6. 5.6Discrete dynamical systems
  7. 5.7Applications to differential equations
  8. 5.8Iterative estimates for eigenvalues
  9. 5.9Markov chains

Chapter 6: Orthogonality and Least Squares

  1. 6.1Inner product, length, and orthogonality
  2. 6.2Orthogonal sets
  3. 6.3Orthogonal projections
  4. 6.4The Gram-Schmidt process
  5. 6.5Least-squares problems
  6. 6.6Machine learning and linear models
  7. 6.7Inner product spaces
  8. 6.8Applications of inner product spaces

Chapter 7: Symmetric Matrices and Quadratic Forms

  1. 7.1Diagonalization of symmetric matrices
  2. 7.2Quadratic forms
  3. 7.3Constrained optimization
  4. 7.4The singular value decomposition
  5. 7.5Applications to image processing and statistics