Revision as of 18:43, 23 June 2011

Working page for the Linear Algebra group at PREP 2011

Vectors
- Geometric objects - lines and planes
- Dot product
- Projection
- Orthogonal decomposition
Systems of equations and elimination
- Free variables
- Consistency of solutions
- Gaussian elimination
Matrix operations and algebra
- Matrix arithmetic
- Matrix inverse
- Matrix equations
- Determinant
- Elementary Matrices
- LU
Vector Space Preliminaries
- Definition of a vector space
- 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
- geometric examples
Linear transformations
- Matrix of a linear transformation
- Reflections, rotations, dilations and projections
- Inverse of a transformation
- kernel, range, injection, surjection
Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory
- Approximation of a function by a Fourier polynomial
Eigenvalues and eigenvectors
- Finding eigenvalues and eigenvectors
- Eigenspaces
- Diagonalization
- Symmetric matrices
- Quadratic forms
Inner product spaces and abstract vector spaces

@@ Line 40: / Line 40: @@
 ** Simplex method
 ** Graph theory
+** Approximation of a function by a Fourier polynomial
 * Eigenvalues and eigenvectors
 ** Finding eigenvalues and eigenvectors
@@ Line 45: / Line 46: @@
 ** Diagonalization
 ** Symmetric matrices
+** Quadratic forms
 * Inner product spaces and abstract vector spaces