Date |
Content of the Lecture |
Assignments/Readings/Notes |
| Lecture 1: 27/7 (Mon) |
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| Lecture 2: 28/7 (Tue) |
Numerical Linear Algebra
- Matrix: trace, determinant, rank, matrix multiplication
- Geometric meaning of a matrix, systems of linear equations and a linear least squares problem
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| Lecture 3: 30/7 (Thurs) |
- Translations as a matrix
- Derivation of linear least squares
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| Lecture 4: 1/8 (Sat) |
- Derivation of linear least squares
- Linearly dependent and linearly independent vectors, rank of a matrix
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| Lecture 5: 3/8 (Mon) |
- MATLAB tutorial: code vectorization, matrix and vector operations, plotting of functions (plot, surf, surfc)
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| Lecture 6: 4/8 (Tue) |
- Matrix rank
- Nullspace and column-space of a matrix; homogeneous linear systems
- Orthogonal matrices
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| Lecture 7: 6/8 (Thurs) |
- Orthogonal matrices
- Discrete Cosine transform matrix
- Vector norms
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| Lecture 8: 8/8 (Sat) |
- Vector norms
- Matrix norms, induced norms, condition number, stability of a linear system Ax = b given errors in b
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| Lecture 9: 10/8 (Mon) |
- Stability of a linear system Ax = b given errors in A
- Eigenvectors and eigenvalues, eigenvvalue multiplicity, physical examples of eigenvectors and eigenvalues
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| Lecture 10: 11/8 (Tue) |
- Properties of eigenvectors and eigenvalues
- Power iteration algorithm for finding the dominant eigenvector
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| Lecture 11: 13/8 (Thurs) |
- Properties of eigenvectors and eigenvalues of symmetric matrices
- Singular value decomposition of a matrix: introduction
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| Lecture 12: 24/8 (Mon) |
- Singular value decomposition of a matrix: introduction, derivation
- Eckart-Young theorem, SVD in image compression, reduced form of SVD, geometric interpretation of SVD
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| Lecture 13: 25/8 (Tue) |
- Orthogonal procrustes algorithm: derivation, extension to estimate translations (with derivation); extension for the case of rotation matrices (result without derivation)
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| Lecture 14: 27/8 (Thurs) |
- SVD applications for: pseudo-inverse or inverse, rank, matrix nullspace, Frobenius norm
- Introduction to structure from motion
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| Lecture 15: 31/8 (Mon) |
- SVD application for nullspace computation
- Introduction to structure from motion: rank theorem, use of SVD
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| Lecture 16: 1/9 (Tue) |
- Structure from motion: rank theorem, use of SVD, algorithm
- LU decomposition/Gaussian elimination for solving linear simultaneous equations
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| Lecture 17: 3/9 (Thurs) |
- Cholesky decomposition, solving banded linear systems
- Principal Components Analysis: concept, derivation, applications to face recognition
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| Lecture 18: 7/9 (Mon) |
- Principal Components Analysis: applications to face recognition, efficient algorithm that side-steps creation of a covariance matrix, choice of k using cross-validation, derivation of multiple, mutually perpendicular directions
- Concept of eigenvalue of covariance matrix as the variance of an eigencoefficient
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| Lecture 19: 8/9 (Tue) |
- Principal Components Analysis: applications to face recognition
- QR decomposition of a matrix and Gram-Schmidt orthogonalization
- Cholesky decomposition of a positive semi-definite matrix
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