Difference between revisions of "Prep 2011 workshop Linear Algebra"
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* Vectors |
* Vectors |
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** Geometric objects - lines and planes |
** Geometric objects - lines and planes |
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| − | * Elimination |
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| + | ** Dot product |
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| − | ** Systems of equations |
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| + | ** Projection |
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| + | ** Orthogonal decomposition |
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| + | * Systems of equations and elimination |
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| + | ** Free variables |
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| + | ** Consistency of solutions |
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** Gaussian elimination |
** Gaussian elimination |
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* Matrix operations and algebra |
* Matrix operations and algebra |
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Revision as of 14:05, 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
