Difference between revisions of "Prep 2011 workshop Linear Algebra Assignment Status"
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| Row operations and Row Echelon Form || 11 || || 2011-06-25 || |
| Row operations and Row Echelon Form || 11 || || 2011-06-25 || |
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− | | Gaussian elimination (Free variables & Consistency of solutions) || 27 || || 2011-06-25 || |
+ | | Gaussian elimination (Free variables & Consistency of solutions) || 27 || || 2011-06-25 || |
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+ | | Rank of a Matrix || || || || There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations |
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| colspan="5" | '''Matrix operations and algebra''' |
| colspan="5" | '''Matrix operations and algebra''' |
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| Linear independence || || || || |
| Linear independence || || || || |
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− | | Basis and |
+ | | Basis and dimension || || || || |
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| Coordinate vectors and change of basis || || || || |
| Coordinate vectors and change of basis || || || || |
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− | | Row space, column space, and null space || || || || |
+ | | Row space, column space, and null space. Rank and Nullity || || || || |
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− | | Dimension and rank || || || || There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations |
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| Geometric examples || || || || |
| Geometric examples || || || || |
Revision as of 20:41, 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 | |||
Rank of a Matrix | There are some "rank" problems in the NPL in Linear Algebra/Matrices/Matrix Operations | ||||
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 dimension | |||||
Coordinate vectors and change of basis | |||||
Row space, column space, and null space. Rank and Nullity | |||||
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 | 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 | ||||
QR Factorization | |||||
Diagonalization of Symmetric Matrices | |||||