Difference between revisions of "Prep 2011 workshop Linear Algebra"

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* Vectors
  
* Vectors
 
** Geometric objects - lines and planes
  
** Geometric objects - lines and planes
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** Dot product
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** Dot product and Vector Projections
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** 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
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*** Note: There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
 
 
** Geometric examples
  
** Geometric examples
 
* Linear transformations
  
* Linear transformations
  +
** 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
 +
** 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 ==
  +
* [[User:AlinaDuca|Alina Duca]]
  +
* [[User:William D. Emerson|William Emerson]]
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* [[User:Tuco|Jim Fischer]]
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* [[User:Tbflowers|Tim Flowers]]
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* [[User:Charles Fortin|Charles Fortin]]
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* [[User:Malcolm|Malcolm Harper]]
  +
  +
== Assignment Status ==
  +
[[Prep_2011_workshop_Linear_Algebra_Assignment_Status]]
  +
  +
  +
== Draft of Documentation documents ==
  +
[[Prep_2011_workshop_Linear_Algebra_Documentation_Draft]]
  +
  +
[[Category:PREP 2011]]

Latest revision as of 13:26, 16 June 2021

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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