Prep 2011 workshop Linear Algebra

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* Vectors
 
* Vectors
 
** Geometric objects - lines and planes
 
** Geometric objects - lines and planes
** Dot product
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** Dot product and Vector Projections
** Projection
+
 
** Orthogonal decomposition
 
** Orthogonal decomposition
 
* Systems of equations and elimination
 
* Systems of equations and elimination
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** Matrix inverse
 
** Matrix inverse
 
** Matrix equations
 
** Matrix equations
** Determinant
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** Determinant and Cramer's Rule
 
** Elementary matrices and LU Decomposition
 
** Elementary matrices and LU Decomposition
*** Note: There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants
 
 
* Vector space preliminaries
 
* Vector space preliminaries
 
** Definition of a vector space and subspaces
 
** Definition of a vector space and subspaces
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** Row space, column space, and null space
 
** Row space, column space, and null space
 
** Dimension and rank
 
** Dimension and rank
*** Note: There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
 
** Geometric examples
 
** 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
 
** Reflections, rotations, dilations and projections
 
** Reflections, rotations, dilations and projections
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** Kernel, range, injection, surjection
 
** Kernel, range, injection, surjection
 
* Applications
 
* Applications
** 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
** Graph theory
 
 
** Approximation of a function by a Fourier polynomial
 
** Approximation of a function by a Fourier polynomial
 
* Eigenvalues and eigenvectors
 
* Eigenvalues and eigenvectors
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** Diagonalization
 
** Diagonalization
 
** Symmetric matrices & Trace  
 
** Symmetric matrices & Trace  
*** Note:  There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
 
** Quadratic forms
 
** Quadratic forms
 
* Inner product spaces and abstract vector spaces
 
* Inner product spaces and abstract vector spaces
 
  
 
== Working group members ==
 
== Working group members ==
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* [[User:Charles Fortin|Charles Fortin]]
 
* [[User:Charles Fortin|Charles Fortin]]
 
* [[User:Malcolm|Malcolm Harper]]
 
* [[User:Malcolm|Malcolm Harper]]
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 +
== Assignment Status ==
 +
[[Prep_2011_workshop_Linear_Algebra_Assignment_Status]]
 +
 +
 +
== Draft of Documentation documents ==
 +
[[Prep_2011_workshop_Linear_Algebra_Documentation_Draft]]

Latest revision as of 15:32, 22 July 2011

Contents

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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