# Prep 2011 workshop Linear Algebra

From WeBWorK

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** Graph theory | ** Graph theory | ||

* Eigenvalues and eigenvectors | * Eigenvalues and eigenvectors | ||

+ | ** Diagonalization | ||

+ | ** Symmetric matrices | ||

* Inner product spaces and abstract vector spaces | * Inner product spaces and abstract vector spaces |

## Revision as of 13:23, 23 June 2011

2011-06-23 !Preliminary Topic List

- 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

- Eigenvalues and eigenvectors
- Diagonalization
- Symmetric matrices

- Inner product spaces and abstract vector spaces