Prep 2011 workshop Linear Algebra: Difference between revisions
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** LU | ** LU | ||
* Vector Space Preliminaries | * Vector Space Preliminaries | ||
** Definition of a vector space | |||
** Euclidean vector spaces | |||
** Span | ** Span | ||
** linear independence | ** linear independence | ||
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** dimension | ** dimension | ||
** geometric examples | ** geometric examples | ||
* Linear transformations | * Linear transformations | ||
** Matrix of a linear transformation | |||
** Geometric transformations | |||
* Applications | * Applications | ||
** Adjacency matrix | ** Adjacency matrix | ||
Revision as of 18:10, 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
- Definition of a vector space
- Euclidean vector spaces
- Span
- linear independence
- basis and orthogonal basis
- row space
- column space
- null space
- dimension
- geometric examples
- Linear transformations
- Matrix of a linear transformation
- Geometric 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