Difference between revisions of "Prep 2011 workshop Linear Algebra"
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** Kernel, range, injection, surjection |
** Kernel, range, injection, surjection |
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* Applications |
* Applications |
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| − | ** Adjacency matrix |
+ | ** Graph theory: Adjacency matrix and Incidence Matrix |
** Least squares |
** Least squares |
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** Curve/surface fitting |
** Curve/surface fitting |
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** Mixture problems |
** Mixture problems |
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** Simplex method |
** Simplex method |
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| − | ** Graph theory |
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** Approximation of a function by a Fourier polynomial |
** Approximation of a function by a Fourier polynomial |
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* Eigenvalues and eigenvectors |
* Eigenvalues and eigenvectors |
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** Quadratic forms |
** Quadratic forms |
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* Inner product spaces and abstract vector spaces |
* Inner product spaces and abstract vector spaces |
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| − | |||
== Working group members == |
== Working group members == |
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Revision as of 16:32, 22 July 2011
Contents
Working page for the Linear Algebra group at PREP 2011
Preliminary Topic List - 2011-06-23
- Vectors
- Geometric objects - lines and planes
- Dot product and Vector Projections
- 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 and Cramer's Rule
- Elementary matrices and LU Decomposition
- Vector space preliminaries
- Definition of a vector space and subspaces
- 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
- Definition of a linear transformation
- Matrix of a linear transformation
- Reflections, rotations, dilations and projections
- Inverse of a transformation
- Kernel, range, injection, surjection
- Applications
- Graph theory: Adjacency matrix and Incidence Matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Approximation of a function by a Fourier polynomial
- Eigenvalues and eigenvectors
- Finding eigenvalues and eigenvectors
- Eigenspaces
- Diagonalization
- Symmetric matrices & Trace
- Quadratic forms
- Inner product spaces and abstract vector spaces
Working group members
Assignment Status
Prep_2011_workshop_Linear_Algebra_Assignment_Status
