Difference between revisions of "Prep 2011 workshop Linear Algebra"
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** Simplex method |
** Simplex method |
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** Graph theory |
** Graph theory |
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+ | ** Approximation of a function by a Fourier polynomial |
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* Eigenvalues and eigenvectors |
* Eigenvalues and eigenvectors |
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** Finding eigenvalues and eigenvectors |
** Finding eigenvalues and eigenvectors |
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** Diagonalization |
** Diagonalization |
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** Symmetric matrices |
** Symmetric matrices |
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+ | ** Quadratic forms |
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* Inner product spaces and abstract vector spaces |
* Inner product spaces and abstract vector spaces |
Revision as of 14:43, 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