Prep 2011 workshop Linear Algebra

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* Vectors
 
* Vectors
 
** Geometric objects - lines and planes
 
** Geometric objects - lines and planes
* Elimination
+
** Dot product
** Systems of equations
+
** Projection
 +
** Orthogonal decomposition
 +
* Systems of equations and elimination
 +
** Free variables
 +
** Consistency of solutions
 
** Gaussian elimination
 
** Gaussian elimination
 
* Matrix operations and algebra
 
* Matrix operations and algebra

Revision as of 13:05, 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
    • Determinant
    • Elementary Matrices
    • LU
  • Vector Space Preliminaries
    • Span
    • linear independence
    • basis and orthogonal basis
    • row space
    • column space
    • null space
    • dimension
    • geometric examples
  • Euclidean vector spaces
  • Linear transformations
  • Applications
    • Adjacency matrix
    • Least squares
    • Curve/surface fitting
    • Mixture problems
    • Simplex method
    • Graph theory
  • Eigenvalues and eigenvectors
  • Inner product spaces and abstract vector spaces
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