Difference between revisions of "Prep 2011 workshop Linear Algebra"

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Preliminary Topic List
  
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= Working page for the Linear Algebra group at PREP 2011 =
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== Preliminary Topic List - 2011-06-23 ==
 
* Vectors
  
* Vectors
 
** Geometric objects - lines and planes
  
** Geometric objects - lines and planes
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** Dot product
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** Dot product and Vector Projections
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** Projection
  
 
** Orthogonal decomposition
  
** Orthogonal decomposition
 
* Systems of equations and elimination
  
* Systems of equations and elimination
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** Free variables
  
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** Row operations and Row Echelon Form
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** Consistency of solutions
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** Gaussian elimination (Free variables & Consistency of solutions)
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** Gaussian elimination
  
 
* Matrix operations and algebra
  
* Matrix operations and algebra
 
** Matrix arithmetic
  
** Matrix arithmetic
 
** Matrix inverse
  
** Matrix inverse
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** Determinant
  
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** Matrix equations
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** Elementary Matrices
  
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** Determinant and Cramer's Rule
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** LU
  
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** Elementary matrices and LU Decomposition
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* Vector Space Preliminaries
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* Vector space preliminaries
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** Definition of a vector space
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** Definition of a vector space and subspaces
 
** Euclidean vector spaces
  
** Euclidean vector spaces
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** Span
  
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** Linear combinations and span
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** linear independence
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** Linear independence
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** basis and orthogonal basis
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** Basis and orthogonal basis
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** row space
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** Coordinate vectors and change of basis
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** column space
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** Row space, column space, and null space
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** null space
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** Dimension and rank
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** dimension
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** Geometric examples
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** geometric examples
  
 
* Linear transformations
  
* Linear transformations
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** Definition of a linear transformation
 
** Matrix of a linear transformation
  
** Matrix of a linear transformation
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** Geometric transformations
  
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** Reflections, rotations, dilations and projections
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** Inverse of a transformation
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** Kernel, range, injection, surjection
 
* Applications
  
* Applications
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** Adjacency matrix
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** 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
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** Graph theory
  
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** Approximation of a function by a Fourier polynomial
 
* Eigenvalues and eigenvectors
  
* Eigenvalues and eigenvectors
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** Finding eigenvalues and eigenvectors
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** Eigenspaces
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** Diagonalization
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** Symmetric matrices & Trace
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** Quadratic forms
 
* Inner product spaces and abstract vector spaces
  
* Inner product spaces and abstract vector spaces
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== Working group members ==
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* [[User:AlinaDuca|Alina Duca]]
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* [[User:William D. Emerson|William Emerson]]
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* [[User:Tuco|Jim Fischer]]
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* [[User:Tbflowers|Tim Flowers]]
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* [[User:Charles Fortin|Charles Fortin]]
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* [[User:Malcolm|Malcolm Harper]]
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== Assignment Status ==
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[[Prep_2011_workshop_Linear_Algebra_Assignment_Status]]
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  +
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== Draft of Documentation documents ==
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[[Prep_2011_workshop_Linear_Algebra_Documentation_Draft]]
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  +
[[Category:PREP 2011]]

Latest revision as of 13:26, 16 June 2021

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


Draft of Documentation documents

Prep_2011_workshop_Linear_Algebra_Documentation_Draft

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