Prep 2011 workshop Linear Algebra

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2011-06-23
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= Working page for the Linear Algebra group at PREP 2011 =
!Preliminary Topic List
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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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** Graph theory
 
** Graph theory
 
* Eigenvalues and eigenvectors
 
* Eigenvalues and eigenvectors
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** Finding eigenvalues and eigenvectors
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** Eigenspaces
 
** Diagonalization
 
** Diagonalization
 
** Symmetric matrices
 
** Symmetric matrices
 
* Inner product spaces and abstract vector spaces
 
* Inner product spaces and abstract vector spaces

Revision as of 13:27, 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
  • Eigenvalues and eigenvectors
    • Finding eigenvalues and eigenvectors
    • Eigenspaces
    • Diagonalization
    • Symmetric matrices
  • Inner product spaces and abstract vector spaces
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