ModelCourses/Linear Algebra

Model Courses/ Linear Algebra

Preliminary Topic List - 2011-06-23

• Vectors
  • Geometric objects - lines and planes
  • Dot product and Vector Projections
  • Orthogonal decomposition
• Systems of equations and elimination
  • Row operations and Row Echelon Form
  • Gaussian elimination (Free variables & Consistency of solutions)
• Matrix operations and algebra
  • Matrix arithmetic
  • Matrix inverse
  • Matrix equations
  • Determinant and Cramer's Rule
  • Elementary matrices and LU Decomposition
• Vector space preliminaries
  • Definition of a vector space and subspaces
  • Euclidean vector spaces
  • Linear combinations and span
  • Linear independence
  • Basis and orthogonal basis
  • Coordinate vectors and change of basis
  • Row space, column space, and null space
  • Dimension and rank
  • Geometric examples
• Linear transformations
  • Definition of a linear transformation
  • Matrix of a linear transformation
  • Reflections, rotations, dilations and projections
  • Inverse of a transformation
  • Kernel, range, injection, surjection
• Applications
  • Graph theory: Adjacency matrix and Incidence Matrix
  • Least squares
  • Curve/surface fitting
  • Mixture problems
  • Simplex method
  • Approximation of a function by a Fourier polynomial
• Eigenvalues and eigenvectors
  • Finding eigenvalues and eigenvectors
  • Eigenspaces
  • Diagonalization
  • Symmetric matrices & Trace
  • Quadratic forms
• Inner product spaces and abstract vector spaces

Working group members

• Alina Duca
• William Emerson
• Jim Fischer
• Tim Flowers
• Charles Fortin
• Malcolm Harper

Instructions for Importing and Exporting Problem Sets

Instructions for importing problem sets

Instructions for exporting problem sets