Prep 2011 workshop Linear Algebra

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** Matrix arithmetic
 
** Matrix arithmetic
 
** Matrix inverse
 
** Matrix inverse
 +
** Matrix equations
 
** Determinant
 
** Determinant
 
** Elementary Matrices
 
** Elementary Matrices
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** Definition of a vector space
 
** Definition of a vector space
 
** Euclidean vector spaces
 
** Euclidean vector spaces
** Span
+
** linear combinations and span
 
** linear independence
 
** linear independence
 
** basis and orthogonal basis
 
** basis and orthogonal basis
** row space
+
** coordinate vectors and change of basis
** column space
+
** row space, column space, and null space
** null space
+
 
** dimension
 
** dimension
 
** geometric examples
 
** geometric examples
 
* Linear transformations
 
* Linear transformations
 
** Matrix of a linear transformation
 
** Matrix of a linear transformation
** Geometric transformations
+
** Reflections, rotations, dilations and projections
 +
** Inverse of a transformation
 
* Applications
 
* Applications
 
** Adjacency matrix
 
** Adjacency matrix

Revision as of 13:16, 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
    • 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
  • 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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