ModelCourses/Linear Algebra: Difference between revisions
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[ | = 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 == | |||
* [[User:AlinaDuca|Alina Duca]] | |||
* [[User:William D. Emerson|William Emerson]] | |||
* [[User:Tuco|Jim Fischer]] | |||
* [[User:Tbflowers|Tim Flowers]] | |||
* [[User:Charles Fortin|Charles Fortin]] | |||
* [[User:Malcolm|Malcolm Harper]] | |||
=[[ModelCourses|Other Model Courses]]= | =[[ModelCourses|Other Model Courses]]= | ||
Revision as of 17:06, 21 December 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 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