**Textbook:** *Linear Algebra* (fifth edition) by O. Bretscher.

**Instructor:** Monica Visan, 6167 Math Sciences Building.

**Office Hours:** Tuesday 10am-12pm or by
appointment.

**Exams:**

**Midterm 1:**Wednesday, February 8th, in class.**Midterm 2:**Wednesday, March 1st, in class.**Final:**Thursday, March 23rd, 8:00-11:00am.

**Midterm 1:** will cover the material presented in
the first 11 lectures; see the table below. You can find a practice midterm
here.

**Midterm 2:** will cover all the material
presented in the first 19 lectures; see the table
below. You can find a practice midterm here.

**Final:** will cover all the material
presented this quarter. You can find a practice final here.

**Homework:** There will be weekly homework.
It is due *in class* on Fridays. It will be posted on this webpage the weekend before
it is due. Further information is given below.

- No late homework will be accepted.
- The reader will grade three problems, each out of five points.
- Up to five further points will be awarded based on the proportion of the remaining problems that are completed.
- Write your name, ID number, and TA section at the top of the first page.
- Staple your pages!
- Homework will be returned in TA section.
- The weakest homework score will be omitted.
- While you may collaborate on the homework, the final version needs to
be written in your own words. The loaning or copying of solutions is
**strictly forbidden**.

**Grading:** Homework: 10%; Midterm 1: 20%; Midterm 2: 20%; Final: 50%. No exceptions.

**Teaching Assistants:**

**Syllabus:** The following table will be updated as we progress through the course.

Lecture |
Book Sections |
Topics |

1 | 1.1-2 | Linear systems, Gauss-Jordan elimination |

2 | 1.3 | Gauss-Jordan elimination, matrix algebra |

3 | 2.1-2 | Linear transformations |

4 | 2.2 | Linear transformations in Geometry |

5 | 2.3 | Matrix algebra, products |

6 | 2.3-4 | Matrix algebra, inverses |

7 | 2.4, 3.1-2 | Matrix inverses, kernel and image of linear transformations, subspaces of R^{n} |

8 | 3.1-2 | Linear independence, bases |

9 | 3.1-3 | Linear independence, bases for the kernel and image of a linear transformation, dimension. |

10-11 | 3.4 | Coordinates |

12 | 5.1-2 | Orthogonality, orthonormal bases, Gram-Schmidt process |

13 | 5.2 | Gram-Schmidt process, QR-factorization |

14 | 5.1 and 5.4 | Orthogonal projection, least squares methods |

15 | 5.1-4 | Orthogonal transformations, orthogonal matrices |

16-19 | 6.1-3 | Determinants |

20 | 7.1-2 | Eigenvalues and eigenvectors, computing eigenvalues |

21-22 | 7.3 | Computing eigenvectors, diagonalization of matrices |

23-26 | 8.1-3 | Symmetric matrices, quadratic forms, SVD (singular-value decomposition) |

**Homework Problems:**

- Homework 1 is due Friday, Jan. 13th, in class.
- Homework 2 is due Friday, Jan. 20th, in class.
- Homework 3 is due Friday, Jan. 27th, in class.
- Homework 4 is due Friday, Feb. 3rd, in class.
- Homework 5 is due Friday, Feb. 10th, in class.
- Homework 6 is due Friday, Feb. 17th, in class.
- Homework 7 is due Friday, Feb. 24th, in class.
- Homework 8 is due Friday, Mar. 3rd, in class.
- Homework 9 is due Friday, Mar. 10th, in class.
- Homework 10. Do not submit it for grading.