Prep 2011 workshop Linear Algebra

From WeBWorK
(Difference between revisions)
Jump to: navigation, search
(Create page from discussions)
(Preliminary Topic List - 2011-06-23)
 
(26 intermediate revisions by 4 users not shown)
Line 1: Line 1:
Preliminary Topic List
+
= Working page for the Linear Algebra group at PREP 2011 =
 +
 
 +
== Preliminary Topic List - 2011-06-23 ==
 
* Vectors
 
* Vectors
 
** Geometric objects - lines and planes
 
** 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 operations and algebra
** Determinant
+
** Matrix arithmetic
** Elementary Matrices
+
** Matrix inverse
** LU/QR
+
** Matrix equations
* Elimination
+
** Determinant and Cramer's Rule
** Systems of equations
+
** Elementary matrices and LU Decomposition
** Gaussian elimination
+
* Vector space preliminaries
* Vector Space Preliminaries
+
** Definition of a vector space and subspaces
** Span
+
** Euclidean vector spaces
** linear independence
+
** Linear combinations and span
** basis and orthogonal basis
+
** Linear independence
** row space
+
** Basis and orthogonal basis
** column space
+
** Coordinate vectors and change of basis
** null space
+
** Row space, column space, and null space
** dimension
+
** Dimension and rank
** geometric examples
+
** Geometric examples
* Euclidean vector spaces
+
 
* Linear transformations
 
* 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
 
* 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 ==
 +
* [[User:AlinaDuca|Alina Duca]]
 +
* [[User:William D. Emerson|William Emerson]]
 +
* [[User:Tuco|Jim Fischer]]
 +
* [[User:Tbflowers|Tim Flowers]]
 +
* [[User:Charles Fortin|Charles Fortin]]
 +
* [[User:Malcolm|Malcolm Harper]]
 +
 +
== 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

follow us