18.06 Linear Algebra

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You can often find the current semester of 18.06 at MIT hosted on the 18.06 github web page.

The github page includes not only exercises and exams, but also lecture summaries, notes, and computational examples using the Julia language.

We have also collected archived problem sets and exams, with solutions from many previous semesters of 18.06 at MIT.

You can also find archived materials from a few semesters on the 18.06 OpenCourseWare page, which also includes lecture videos.

Many people watch Gil Strang's 18.06 (Spring 2005) lecture videos on YouTube, which can also be found on OpenCourseWare. For ease of access, we link the videos by topic below.

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!) |