# Prep 2011 workshop Linear Algebra

From WeBWorK

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** Matrix arithmetic | ** Matrix arithmetic | ||

** Matrix inverse | ** Matrix inverse | ||

+ | ** Matrix equations | ||

** Determinant | ** Determinant | ||

** Elementary Matrices | ** Elementary Matrices | ||

Line 18: | Line 19: | ||

** Definition of a vector space | ** Definition of a vector space | ||

** Euclidean vector spaces | ** Euclidean vector spaces | ||

− | ** | + | ** linear combinations and span |

** linear independence | ** linear independence | ||

** basis and orthogonal basis | ** basis and orthogonal basis | ||

− | ** | + | ** coordinate vectors and change of basis |

− | ** column space | + | ** row space, column space, and null space |

− | + | ||

** dimension | ** dimension | ||

** geometric examples | ** geometric examples | ||

* Linear transformations | * Linear transformations | ||

** Matrix of a linear transformation | ** Matrix of a linear transformation | ||

− | ** | + | ** Reflections, rotations, dilations and projections |

+ | ** Inverse of a transformation | ||

* Applications | * Applications | ||

** Adjacency matrix | ** Adjacency matrix |

## Revision as of 13:16, 23 June 2011

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

- Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory

- Eigenvalues and eigenvectors
- Inner product spaces and abstract vector spaces