Linear Algebra 2016


Professor János Pach


Frank de Zeeuw – Björn Andersson – Marcel Hildebrandt – Zsolt Lángi – Nicolò Sitzia – Fan Zhang

If you have any questions, please email Frank.

Time and place

– Lectures:
     – Tuesday: CO2, 13:00-15:00;
     – Thursday: CE3, 14:00-16:00.

– Exercise sessions:
     – Tuesday: CM1104 / CM1105 / CM1106, 15:00-16:00; (GCA331 is on the schedule but is not used)
     – Thursday: CM1120 / CM1121, 16:00-17:00.

Syllabus and schedule

Here is the official course information.

Textbook: Lay, Linear Algebra and its Applications (4th edition)

We will cover the following sections from the book:

Week 1: 1.1, 1.2, 1.3, 1.4; Row reduction, vector and matrix notation, span, parametric vector form.

Week 2: 1.5, 1.7, 1.8, 1.9; Homogeneous systems, linear independence, linear transformations.

Week 3: 1.8, 1.9, 2.1; Linear transformations, matrix multiplication.

Week 4: 2.2, 2.3; Invertible matrices and the Invertible Matrix Theorem.

Week 5: 2.4, 2.5, (2.6); Block matrices, LU factorization, (Leontief model).

Week 6: 3.1, 3.2, 3.3; Determinants.

Week 7: 4.1, 4.2, 4.3; Vector spaces, subspaces, null spaces, column spaces, bases.

Week 8: Tuesday: Practice exam. Thursday: 4.3; Bases.

Week 9: 4.4, 4.5, 4.6, 4.7, 5.1; Coordinate systems, dimension, rank, change of basis, eigenvectors and eigenvalues.

Week 10: 5.2, 5.3, 5.4; Characteristic equation, diagonalization, change of basis.

Week 11: 5.5, 6.1; Complex eigenvalues, inner products.

Week 12: 6.2, 6.3, 6.4; Orthogonal bases, orthogonal projection, Gram-Schmidt, QR factorization.

Week 13: 6.5, 7.1; Least-squares, diagonalization of symmetric matrices.

Week 14: 7.2; Quadratic forms. Review.

Exercise sessions

Here is some information about the exercise sessions.

  • The exercise sets are available on our moodle page. New sets will typically be posted every Monday. Please bring to the exercise session either a paper copy, or an electronic device that you can access the file on.
  • You do not have to hand in solutions to the exercise sets. Their purpose is just to help you learn the material and prepare for the exam.
  • There are no room assignments, so just find a seat in any of the three rooms.
  • There will be several assistants that can answer any questions that you have about the exercises. You are very much encouraged to work together on the exercises.
  • Please note that every week the exercise set is for the whole week, and roughly speaking the first half relates to the first lecture, while the second half relates to the second lecture. So, during the session on Tuesday, you will not yet have all the information for the second half of the exercise set, and with that part you will have to wait until Thursday. You are of course free to do them at your own pace, and we will still answer questions about exercises from previous weeks.
  • Every week, after Thursday’s exercise session, solutions to the exercises will be posted on moodle.