Difference between revisions of "Prep 2011 workshop Linear Algebra"
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** Matrix equations |
** Matrix equations |
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** Determinant |
** Determinant |
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| − | ** Elementary |
+ | ** Elementary matrices |
** LU |
** LU |
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| − | * Vector |
+ | * Vector space preliminaries |
** Definition of a vector space |
** Definition of a vector space |
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** Euclidean vector spaces |
** Euclidean vector spaces |
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| − | ** |
+ | ** 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 |
* Linear transformations |
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** Matrix of a linear transformation |
** Matrix of a linear transformation |
||
** Reflections, rotations, dilations and projections |
** Reflections, rotations, dilations and projections |
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** Inverse of a transformation |
** Inverse of a transformation |
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| − | ** |
+ | ** Kernel, range, injection, surjection |
* Applications |
* Applications |
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** Adjacency matrix |
** Adjacency matrix |
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Revision as of 14:52, 23 June 2011
Working page for the Linear Algebra group at PREP 2011
Preliminary Topic List - 2011-06-23
- 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
- Kernel, range, injection, surjection
- Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory
- Approximation of a function by a Fourier polynomial
- Eigenvalues and eigenvectors
- Finding eigenvalues and eigenvectors
- Eigenspaces
- Diagonalization
- Symmetric matrices
- Quadratic forms
- Inner product spaces and abstract vector spaces
