Prep 2011 workshop Linear Algebra

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** Coordinate vectors and change of basis
 
** Coordinate vectors and change of basis
 
** Row space, column space, and null space
 
** Row space, column space, and null space
** Dimension
+
** Dimension and rank
 
** Geometric examples
 
** Geometric examples
 
* Linear transformations
 
* Linear transformations

Revision as of 12:24, 24 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 and rank
    • 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
    • Approximation of a function by a Fourier polynomial
  • Eigenvalues and eigenvectors
    • Finding eigenvalues and eigenvectors
    • Eigenspaces
    • Diagonalization
    • Symmetric matrices
    • Quadratic forms
  • Inner product spaces and abstract vector spaces
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