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