Difference between revisions of "Prep 2011 workshop Linear Algebra"
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** LU |
** LU |
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* Vector Space Preliminaries |
* Vector Space Preliminaries |
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| + | ** Definition of a vector space |
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| + | ** Euclidean vector spaces |
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** Span |
** Span |
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** linear independence |
** linear independence |
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** dimension |
** dimension |
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** geometric examples |
** geometric examples |
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| − | * Euclidean vector spaces |
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* Linear transformations |
* Linear transformations |
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| + | ** Matrix of a linear transformation |
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| + | ** Geometric transformations |
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* Applications |
* Applications |
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** Adjacency matrix |
** Adjacency matrix |
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Revision as of 14:10, 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
