Revision as of 18:27, 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
Eigenvalues and eigenvectors
- Finding eigenvalues and eigenvectors
- Eigenspaces
- Diagonalization
- Symmetric matrices
Inner product spaces and abstract vector spaces

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+= Working page for the Linear Algebra group at PREP 2011 =
-!Preliminary Topic List
+== Preliminary Topic List - 2011-06-23 ==
 * Vectors
 ** Geometric objects - lines and planes
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 ** Graph theory
 * Eigenvalues and eigenvectors
+** Finding eigenvalues and eigenvectors
+** Eigenspaces
 ** Diagonalization
 ** Symmetric matrices
 * Inner product spaces and abstract vector spaces