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 || || || || |
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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 | |||||
