Difference between revisions of "Prep 2011 workshop Linear Algebra"
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* Systems of equations and elimination |
* Systems of equations and elimination |
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** Row operations and Row Echelon Form |
** Row operations and Row Echelon Form |
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| − | ** Gaussian elimination (Free variables & Consistency of solutions |
+ | ** Gaussian elimination (Free variables & Consistency of solutions) |
* Matrix operations and algebra |
* Matrix operations and algebra |
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** Matrix arithmetic |
** Matrix arithmetic |
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Revision as of 13:38, 24 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
- Row operations and Row Echelon Form
- Gaussian elimination (Free variables & Consistency of solutions)
- 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 and rank
- 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
