Difference between revisions of "Prep 2011 workshop Linear Algebra"
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m (keep editing from discussions) |
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** Matrix arithmetic |
** Matrix arithmetic |
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** Matrix inverse |
** Matrix inverse |
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+ | ** Matrix equations |
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** Determinant |
** Determinant |
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** Elementary Matrices |
** Elementary Matrices |
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** Definition of a vector space |
** Definition of a vector space |
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** Euclidean vector spaces |
** Euclidean vector spaces |
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− | ** Span |
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+ | ** linear combinations and span |
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** linear independence |
** linear independence |
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** basis and orthogonal basis |
** basis and orthogonal basis |
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− | ** row space |
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+ | ** coordinate vectors and change of basis |
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− | ** column space |
+ | ** row space, column space, and null space |
− | ** null space |
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** dimension |
** dimension |
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** geometric examples |
** geometric examples |
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* Linear transformations |
* Linear transformations |
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** Matrix of a linear transformation |
** Matrix of a linear transformation |
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− | ** Geometric transformations |
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+ | ** Reflections, rotations, dilations and projections |
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+ | ** Inverse of a transformation |
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* Applications |
* Applications |
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** Adjacency matrix |
** Adjacency matrix |
Revision as of 14:16, 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
- 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
- Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory
- Eigenvalues and eigenvectors
- Inner product spaces and abstract vector spaces