Prep 2011 workshop Linear Algebra: Difference between revisions
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* Vectors | * Vectors | ||
** Geometric objects - lines and planes | ** Geometric objects - lines and planes | ||
* | ** Dot product | ||
** Systems of equations | ** Projection | ||
** Orthogonal decomposition | |||
* Systems of equations and elimination | |||
** Free variables | |||
** Consistency of solutions | |||
** Gaussian elimination | ** Gaussian elimination | ||
* Matrix operations and algebra | * Matrix operations and algebra | ||
Revision as of 18:05, 23 June 2011
Preliminary Topic List
- 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
- Determinant
- Elementary Matrices
- LU
- Vector Space Preliminaries
- Span
- linear independence
- basis and orthogonal basis
- row space
- column space
- null space
- dimension
- geometric examples
- Euclidean vector spaces
- Linear transformations
- Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory
- Eigenvalues and eigenvectors
- Inner product spaces and abstract vector spaces