Matrices, eigenvectors, diagonalization, orthogonality, linear systems, applications. Intended for Honours students.

Instructor: Jozsef Solymosi

Email: solymosi@math.ubc.ca

Office: MATH 220

Lectures: Mon Wed Fri 10:00 11:00 Leonard S. Klinck 460

Office Hours: Tuesday 2:30-3:45 (or by appointment) MATH 220 (special office hours before midterms)

If you have math questions then you can also visit the Math Learning Centre on weekdays 10 am–5 pm.

Marking: Your mark will be based on homework assignments, two midterm exams and one final exam, weighted as follows:

• Homework: 20%

• Midterm I: 15%

• Midterm II: 15%

• Final Exam: 50%

No late homework will be accepted.

Exams: The midterm exams are scheduled as follows:

• Midterm I: Wednesday, February 7. (10:00-10:50 in class)

Special office hours: February 6 Tuesday 16:00-17:30 in LSK 300C (no office hours 2:30-3:45 in MATH 220)

Arrive at least 5 minutes before class. Use every other seats in the classroom.

To see the questions, Click here!

Check the HW questions! The test problems will be similar to some HW questions.

• Midterm II: Friday, March 16.

There will be no notes, books, calculators or "cheat sheets" allowed on any of the

midterms. This holds also for the final exam.

No makeup exams will be given. If you miss a midterm, your final exam will count for

65% of your grade.

Textbook: A. Givental: Linear Algebra and Differential Equations.

(@UBC Bookstore)

We will follow Givental’s book, but there are many other books available. An easy to read text is David C. Lay's Linear Algebra book. Older editions are available under $10. Any edition could be a good second textbook for the course.

Homework Assignments:

- HW 1 The questions are from Givental's book. Exercises 1.1.2.(b), 1.1.3.(a)(b), 1.2.1.(e), 1.2.2.(f). (Due Jan 17 in class)

- HW 2 Click here! (Due Jan 24.)

- HW 3 Click here! (Due Jan 31.)
- HW 4 Click here! (Due Feb 7.)
- HW 5 Click here! (Due Feb 28.)
- HW 6
- HW 7
- HW 8
- HW 9

Below is the syllabus which lists all topics from the book covered in this course.

1. Geometry on the plane.

(11 lectures and 3 homework assignments)

1.1. Vectors

1.1.1. Definitions. 1.1.2. Inner product. 1.1.3. Coordinates.

1.2. Analytical geometry.

1.2.1. Linear functions and straight lines. 1.2.2. Conic sections.

1.2.3. Quadratic forms.

1.3. Linear transformations and matrices.

1.3.1. Linearity. 1.3.2. Composition. 1.3.3. Inverses. 1.3.4. Matrix Zoo.

1.4. Complex numbers.

1.4.1. Definitions and geometrical interpretations. 1.4.2. The exponential function.

1.4.3. The Fundamental Theorem of Algebra.

1.5. Eigenvalues.

1.5.1. Linear systems. 1.5.2. Determinants. 1.5.3. Normal forms.

3. Linear Algebra. (Part 1)

(11 lectures and 3 homework assignments)

3.1. Classical problems of linear algebra

3.2. Matrices and determinants.

3.2.1. Matrix algebra. 3.2.2. The determinant function.

3.2.3. Properties of determinants. 3.2.4. Cofactors.

3.3. Vectors and linear systems.

3.3.1. 3D and beyond. 3.3.2. Linear (in)dependence and bases.

3.3.3. Subspaces and dimension. 3.3.4. The rank theorem and applications.

3.4. Gaussian elimination.

3.4.1. Row reduction. 3.4.2. Applications.

Linear Algebra. (Part 2)

(11 lectures and 3 homework assignments)

3. 5. Quadratic forms.

3.5.1. Inertia indices. 3.5.2. Least square fitting to data. 3.5.3. Orthonormal bases.

3.5.4. Orthogonal diagonalization. 3.5.5. Small oscillations.

3. 6. Eigenvectors.

3.6.1. Diagonalization theorem.

3.6.2. Linear ODE systems.