Prep 2011 workshop Linear Algebra: Difference between revisions
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** Matrix equations | ** Matrix equations | ||
** Determinant | ** Determinant | ||
** Elementary | ** Elementary matrices | ||
** LU | ** LU | ||
* Vector | * Vector space preliminaries | ||
** Definition of a vector space | ** Definition of a vector space | ||
** Euclidean vector spaces | ** 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 | * Linear transformations | ||
** Matrix of a linear transformation | ** Matrix of a linear transformation | ||
** Reflections, rotations, dilations and projections | ** Reflections, rotations, dilations and projections | ||
** Inverse of a transformation | ** Inverse of a transformation | ||
** | ** Kernel, range, injection, surjection | ||
* Applications | * Applications | ||
** Adjacency matrix | ** Adjacency matrix | ||
Revision as of 18:52, 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