18.06 Linear Algebra, Spring 2019

(under construction February 3, 2019)

Lecture Summaries | Problem Sets and Exams | Stellar | Syllabus | Archived Psets/Exams | Piazza | Julia |

Videos may be found on the MIT Open Course Ware (OCW) website:

http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm

Many people watch the lecture videos on YouTube:

Lectures by Gil Strang: MIT 18.06 (Spring 2005) on YouTube - scroll to bottom of this page for overview of videos by topic.

You may find the lectures more exciting when you watch them at 1.5x or 2x the normal speed (keeping the pitch of your voice constant). It is good for a quick review too. You may follow the the link below to set up your media player.

http://sites.google.com/site/variablespeedlectures/ (The VLC player can be used for speeding up YouTube videos too: Simply paste the URL into VLC)

Lecture #1: The Geometry of Linear Equations (Watch!) | Lecture #19: Determinant Formulas and Cofactors (Watch!) |

Lecture #2: Elimination with Matrices (Watch!) | Lecture #20: Cramer's Rule, Inverse Matrix, and Volume (Watch!) |

Lecture #3: Multiplication and Inverse Matrices (Watch!) | Lecture #21: Eigenvalues and Eigenvectors (Watch!) |

Lecture #4: Factorization into A = LU (Watch!) | Lecture #22: Diagonalization and Powers of A (Watch!) |

Lecture #5: Transposes, Permutations, Spaces R^n (Watch!) |
Lecture #23: Differential Equations and exp(At) (Watch!) |

Lecture #6: Column Space and Nullspace (Watch!) | Lecture #24 : Markov Matrices; Fourier Series (Watch!) |

Lecture #7: Solving Ax = 0: Pivot Variables, Special Solutions (Watch!) | Lecture #24b : Quiz 2 Review (Watch!) |

Lecture #8: Solving Ax = b: Row Reduced Form R (Watch!) | Lecture #25 : Symmetric Matrices and Positive Definiteness (Watch!) |

Lecture #9: Independence, Basis, and Dimension (Watch!) |
Lecture #26 : Complex Matrices; Fast Fourier Transform (Watch!) |

Lecture #10: The Four Fundamental Subspaces (Watch!) | Lecture #27 : Positive Definite Matrices and Minima (Watch!) |

Lecture #11: Matrix Spaces; Rank 1; Small World Graphs (Watch!) | Lecture #28 : Similar Matrices and Jordan Form (Watch!) |

Lecture #12: Graphs, Networks, Incidence Matrices (Watch!) | Lecture #29 : Singular Value Decomposition (Watch!) |

Lecture #13: Quiz 1 Review (Watch!) | Lecture #30 : Linear Transformations and Their Matrices (Watch!) |

Lecture #14: Orthogonal Vectors and Subspaces (Watch!) | Lecture #31: Change of Basis; Image Compression (Watch!) |

Lecture #15: Projections onto Subspaces (Watch!) | Lecture #32: Quiz 3 Review (Watch!) |

Lecture #16: Projection Matrices and Least Squares (Watch!) | Lecture #33: Left and Right Inverses; Pseudoinverse (Watch!) |

Lecture #17: Orthogonal Matrices and Gram-Schmidt (Watch!) | Lecture #34: Final Course Review (Watch!) |

Lecture #18: Properties of Determinants (Watch!) |