# Prep 2011 workshop Linear Algebra

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* Vectors | * Vectors | ||

** Geometric objects - lines and planes | ** Geometric objects - lines and planes | ||

− | ** Dot product | + | ** Dot product and Vector Projections |

− | + | ||

** Orthogonal decomposition | ** Orthogonal decomposition | ||

* Systems of equations and elimination | * Systems of equations and elimination | ||

Line 14: | Line 13: | ||

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

** Matrix equations | ** Matrix equations | ||

− | ** Determinant | + | ** Determinant and Cramer's Rule |

− | ** Elementary matrices | + | ** Elementary matrices and LU Decomposition |

− | + | ||

* Vector space preliminaries | * Vector space preliminaries | ||

** Definition of a vector space and subspaces | ** Definition of a vector space and subspaces | ||

Line 28: | Line 26: | ||

** Geometric examples | ** Geometric examples | ||

* Linear transformations | * Linear transformations | ||

+ | ** Definition of a linear transformation | ||

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

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

Line 33: | Line 32: | ||

** Kernel, range, injection, surjection | ** Kernel, range, injection, surjection | ||

* Applications | * Applications | ||

− | ** Adjacency matrix | + | ** Graph theory: Adjacency matrix and Incidence Matrix |

** Least squares | ** Least squares | ||

** Curve/surface fitting | ** Curve/surface fitting | ||

** Mixture problems | ** Mixture problems | ||

** Simplex method | ** Simplex method | ||

− | |||

** Approximation of a function by a Fourier polynomial | ** Approximation of a function by a Fourier polynomial | ||

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

Line 44: | Line 42: | ||

** Eigenspaces | ** Eigenspaces | ||

** Diagonalization | ** Diagonalization | ||

− | ** Symmetric matrices | + | ** Symmetric matrices & Trace |

** Quadratic forms | ** Quadratic forms | ||

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

+ | |||

+ | == Assignment Status == | ||

+ | [[Prep_2011_workshop_Linear_Algebra_Assignment_Status]] | ||

+ | |||

+ | |||

+ | == Draft of Documentation documents == | ||

+ | [[Prep_2011_workshop_Linear_Algebra_Documentation_Draft]] |

## Latest revision as of 15:32, 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