Difference between revisions of "Prep 2011 workshop Linear Algebra Assignment Status"

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| Adjacency matrix || || || ||
 
| Adjacency matrix || || || ||
 
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| Least squares || || || ||
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| Least squares Approximation|| || || || should this be in Inner Product Spaces?
 
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| Curve/surface fitting || || || ||
 
| Curve/surface fitting || || || ||
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| Approximation of a function by a Fourier polynomial || || || ||
 
| Approximation of a function by a Fourier polynomial || || || ||
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| Singular Value Decomposition || || || 2011-06-25 || should this be in Inner Product Spaces?
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| Quadratic Forms || || || ||
 
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| colspan="5" | '''Eigenvalues and eigenvectors'''
 
| colspan="5" | '''Eigenvalues and eigenvectors'''
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| colspan="5" | '''Inner product spaces and abstract vector spaces'''
 
| colspan="5" | '''Inner product spaces and abstract vector spaces'''
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| Inner Product Spaces, Length, Orthogonality || || || ||
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| Orthonormal Bases || || || ||
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| Orthonormal Projections || || || ||
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| Gram-Schmidt Process || || || 2011-06-25 ||
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| Orthogonal Complements || || || ||
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| Diagonalization of Symmetric Matrices || || || ||
 
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| || colspan="3" | We still need sub topics ||
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Revision as of 20:07, 25 June 2011

Current status of Linear Algebra Model Course Assignments

Topic NPL Custom Updated Notes
Vectors
Geometric objects - lines and planes 14 2011-06-25
Dot product and Vector Projections 15 2011-06-25
Orthogonal decomposition
Systems of equations and elimination
Row operations and Row Echelon Form 11 2011-06-25
Gaussian elimination (Free variables & Consistency of solutions) 27 2011-06-25
Matrix operations and algebra
Matrix arithmetic 16 2011-06-25
Matrix inverse 16 2011-06-25
Matrix equations 5 2011-06-25
Determinant and Cramer's Rule 28 2011-06-25 Need to add Cramer's rule Qs
Elementary matrices and LU Decomposition 5 2011-06-25 There are determinant of elementary matrix questions in the NPL in Linear Algebra/Matrices/Determinants
Vector space preliminaries
Definition of a vector space and subspaces 4 2011-06-25
Euclidean vector spaces 4 2011-06-25
Linear combinations and span 6 2011-06-25
Linear independence
Basis and orthogonal basis
Coordinate vectors and change of basis
Row space, column space, and null space
Dimension and rank There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
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 Approximation should this be in Inner Product Spaces?
Curve/surface fitting
Mixture problems
Simplex method
Graph theory
Approximation of a function by a Fourier polynomial
Singular Value Decomposition 2011-06-25 should this be in Inner Product Spaces?
Quadratic Forms
Eigenvalues and eigenvectors
Finding eigenvalues and eigenvectors 12 2011-06-25
Eigenspaces 2011-06-25
Diagonalization 2011-06-25
Symmetric matrices & Trace 2011-06-25 There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations
Quadratic forms 2011-06-25
Inner product spaces and abstract vector spaces
Inner Product Spaces, Length, Orthogonality
Orthonormal Bases
Orthonormal Projections
Gram-Schmidt Process 2011-06-25
Orthogonal Complements
Diagonalization of Symmetric Matrices