## Lectures

Previously: 2016Date | Title | Video | Slides |
---|---|---|---|

Wednesday, 9/6 | Introduction | Video | Slides |

Friday, 9/8 | The Field | Video | Slides |

Monday, 9/11 | The Field (contd.) + The Vector | Video | Slides |

Wednesday, 9/13 | The Vector (contd.) | Video | Slides |

Friday, 9/15 | The Vector (contd.) | Video | Slides |

Monday, 9/18 | The Vector Space | Video | Slides |

Wednesday, 9/20 | The Vector Space (contd.) | Video | Slides |

Friday, 9/22 | The Vector Space (contd.) | Video | Slides |

Monday, 9/25 | The Vector Space, transition to The Matrix | Video | Slides |

Wednesday, 9/27 | The Matrix | Video | Slides |

Friday, 9/29 | The Matrix | Video | Slides |

Monday, 10/2 | The Matrix, Error Correcting Codes | Video | Slides |

Wednesday, 10/4 | Matrices, functions | Video 1 Video 2 | Slides |

Friday, 10/6 | Linear transformations and Matrix Inverses | N/A | Slides |

Wednesday, 10/11 | Coordinate representations, Grow and Shrink algorithm, representing graph edges with vectors | Video | Slides |

Friday, 10/13 | Formulating minimum spanning forest in linear algebra; Linear dependence; Superfluous-Vector Lemma; Linear-Dependence Lemma | Video | Slides |

Monday, 10/16 | Properties of linear (in)dependence; analyzing the grow & shrink algorithms; the basis | Video | Slides |

Wednesday, 10/18 | Basis, unique representation, change of basis | Video | Slides |

Friday, 10/20 | Wiimote whiteboard, Perspective rectification, start of Exchange Lemma | Video | Slides |

Monday, 10/23 | Morphing Lemma, Dimension, Rank, Subset-Basis Lemma, Grow-Algorithm-Termination | Video | Slides |

Wednesday, 10/25 | Superset-Basis Lemma, Dimension Lemma, Rank Theorem, Direct Sum | Video | Slides |

Friday, 10/27 | Direct Sum, Invertibility of a Linear Function, Kernel-Image Theorem, Rank-Nullity Theorem | Video | Slides |

Monday, 10/30 | Matrix invertibility, converting between representations of subspaces | Video | Slides |

Wednesday, 11/1 | Interpretations of vector-matrix multiplication, Developing Gaussian elimination | Video | Slides |

Friday, 11/3 | Gaussian Elimination: Recording the transformation, Algorithm for finding basis of null space | Video | Slides |

Monday, 11/6 | Gaussian elimination, Integer factoring, Inner Product, Norm, Orthogonality | Video | Slides |

Wednesday, 11/8 | Properties of orthogonality, parallel and perpendicular components of a vector, fire engine problem, computing the projections | Video | Slides |

Friday, 11/10 | minimizing sum of squared distances, centroid, k-means, higher-dimensional projection, high-dimensional fire-engine lemma, projecting onto a higher-dimensional space | Video 1 Video 2 | Slides |

Monday, 11/13 | project onto (correct spec and proof of correctness), orthogonalization, nonzero orthogonal vectors are linearly independent | Video | Slides |

Wednesday, 11/15 | matrix form for orthogonalize; computing a basis; find_subset_basis; basis for null space; orthogonal complement | Video | Slides |

Friday, 11/17 | Null space and orthogonal complement; algorithm for computing orthogonal complement; normalization; orthonormal vectors; column-orthogonal and orthogonal matrices, QR factorization | N/A | Slides |

Monday, 11/20 | Using QR factorization to solve a matrix equation when the matrix has linearly independent columns; what if the columns are linearly dependent; the least-squares problem; using QR factorization to solve the least-squares problem when the matrix has linearly independent columns; the normal equations; linear regression; coping with approximate data (improving accuracy of output without more accurate measurements); applications of least squares when columns are linearly dependent | Video | Slides |

Monday, 11/27 | The Singular Value Decomposition: Frobenius norm for matrices, low-rank matrices, the trolley-line-location problem, best rank-one approximation to a matrix | Video | Slides |

Friday, 12/1 | Best rank-one approximation; Closest 1- and k- dimensional vector/affine space; The SVD: deriving it, its existence, its properties; Rank-k approximation in terms of the SVD | Video | Slides |

Monday, 12/4 | Principal Component Analysis using SVD; Uses of SVD; Least squares using SVD | Video | Slides |

Wednesday, 12/6 | Eigenvalues and Eigenvectors, similarity and diagonalizability, criterion for lambda being an eigenvalue of A, linearly independent eigenvectors, first look at power method | Video | Slides |

Friday, 12/8 | Interpretation of eigenvalue analysis using change of basis; simple example of population dynamics; dance-floor dynamics and "forgetting" initial distribution; modeling spatial locality in CPU memory fetches; Markov chains; stationary distributions; power method; power method applied to a Markov chain; Perron-Frobenius Theorem; intro to Pagerank | Video | Slides |

Monday, 12/11 | Pagerank (cont'd); Computing an eigenvalue; Limitations of eigenvector analysis; Eigenvalues for symmetric and asymmetric matrices; Positive definite, positive semi-definite, and determinant; Uses of determinants | Video | Slides |