Linear Algebra II

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About the course

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13-week lesson plan

Course — detailed outline

4. Vector Spaces
   • (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
5. Eigenvalues and Eigenvectors
   • (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
   • (5.8) Iterative Estimates for Eigenvalues
6. Orthogonality and Least Squares
   • (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
7. Symmetric Matrices and Quadratic Forms
   • (7.1) Diagonalization of Symmetric Matrices
   • (7.2) Quadratic Forms
   • (7.3) Constrained Optimization
   • (7.4) The Singular Value Decomposition