Revision as of 13:09, 21 December 2011

Model Courses/ Linear Algebra

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

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-= Working page for the Linear Algebra group at PREP 2011 =
+= Model Courses/ Linear Algebra =
 == Preliminary Topic List - 2011-06-23 ==
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 * [[User:Charles Fortin|Charles Fortin]]
 * [[User:Malcolm|Malcolm Harper]]
+[[ModelCourses/Instructions for importing problem sets|Instructions for importing problem sets]]
+[[ModelCourses/Instructions for exporting problem sets|Instructions for exporting problem sets]]
 =[[ModelCourses|Other Model Courses]]=