Math213BKK
Linear Algebra 2
Faculty
Galina Kaleeva
Data Scientist at Yandex & HSE Lecturer
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course builds on the study of Linear Algebra with a focus on advanced concepts and applications. After a brief review of core topics such as matrices, determinants, and complex numbers, students will explore linear operators, eigenvalues, eigenvectors, and canonical forms, including triangular and Jordan normal forms. The syllabus also covers bilinear and symmetric forms, singular value decomposition, and the pseudoinverse matrix with practical applications. Advanced topics include the Fourier transform, with emphasis on its role in science and machine learning. Practice sessions, a midterm, and a final exam ensure that students consolidate both theoretical understanding and problem-solving skills.
Learning highlights
- Mastery of linear operators – understanding eigenvalues, eigenvectors, diagonalisation, and Jordan normal form.
- Practical skills in advanced matrix decompositions – singular value decomposition and the pseudoinverse, with applications.
- Applications in machine learning and science – using linear algebra techniques in real-world contexts.
Course outline
15 classes
Session 1
Recap: matrices, determinants.
Session 2
Recap: linear operators.
Session 3
Eigenvalues and eigenvectors. Diagonalisable operators.
Session 4
Triangular form of a linear operator. Generalised eigenvectors.
Session 5
Nilpotent operators. Jordan normal form.
Session 6
Practice Session. Review.
Session 7
Midterm
Session 8
Symmetric matrices.
Session 9
Bilinear forms. Positive definite bilinear forms.
Session 10
Singular value decomposition and its applications.
Session 11
Pseudoinverse matrix: definition and properties.
Session 12
Fast Fourier transform.
Session 13
Practice Session. Review.
Session 14
Practice Session. Review.
Session 15
Final exam
Course materials
Books
Methodology
The typical 3-hour session includes a discussion of the theory and problems previously studied and solved independently by the students, a lecture with theoretical explanations and demonstration of problem-solving techniques, and a practical part, where students work on applying the acquired knowledge and solving practical tasks on their own.
Grading
Galina Kaleeva obtained her degree from Lomonosov Moscow State University, where she majored in Mathematics and Mechanics.
Currently, Galina works as a Data Scientist at Yandex, where she puts her analytical skills to create a platform for school students interested in STEM: enables hypothesis generation and validation based on data, extracts insights from big data, and supports management in making decisions related to the EdTech business.
See full profileApply for this course
Linear Algebra 2
by Galina Kaleeva
Total hours
45 Hours
Dates
Jun 08 - Jun 26, 2026
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.