Math201BKK
Linear Algebra 2
Faculty
Andrey Kechin
Master of Science fellow
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course continues with a deeper exploration of linear algebra. The second part is designed for students of machine learning and data analysis. A range of applications aligned with real computational and exploratory scenarios will be studied and applied.
Learning highlights
This course is designed to introduce machine learning and data science students to the core concepts of linear algebra, with a focus on practical applications in computing. Students will learn to work with key matrix methods, including PCA and SVD — essential tools for machine learning and data science.
Key topics include matrix transformations, determinants, eigenvalues, and eigenvectors. The course emphasises algorithmic thinking, with hands-on coding exercises to implement linear algebra methods in Python. Students will explore how linear algebra underpins image recognition, search engines, neural networks, and data processing pipelines.
The course combines classical mathematical problems with real-world examples and projects.
Course outline
15 classes
Session 1
- Vectors
- Vector space
- Vector norms
- Operation on vectors
- Dot product
- Cross product
Session 2
- Geometrical approach to vector operations
- Linear transformations
- Null space
- Kernels
- Range
Session 3
- Matrices
- Operations on matrices
- Determinant of a matrix
- Inverse matrix
- Identity matrix
- Transpose of a matrix
Session 4
- Pseudoinverse matrix
- Orthogonal matrices
- Matrix product
- Practice in matrix multiplication
Session 5
- Linear transformation matrices
- Translation, rotation, amplification, twist
- Amplitwist
Session 6
- Eigenvalues
- Eigenvectors
- Geometrical interpretation
- Pseudoeigen values
Session 7
- Linear operators
- Bilinear forms
- Linear regression
Session 8
Midterm exam
Session 9
- Principal component analysis
- PCA introduction
- PCA in data science
Session 10
- Single value decomposition
- Numpy lib in python
- SVD in data science
Session 11
- Tensors
- Tensor analysis
Session 12
- Function
- Functional analysis
Session 13
- Data fitting
- Exact data fitting
- Approximate data fitting
Session 14
Q&A
Session 15
Final Exam
Methodology
The methodology is based on mixing PBL (problem-based learning) and IVL (interactive and visual learning) technologies. PBL is based on presenting real-world problems and guiding students to apply discrete math concepts like graph theory or combinatorics to solve them. IVL technology considers using visualisation tools in lecture studies. Each class can be divided into three parts: Lection part, Active learning (discussion, Q&A), Problem-solving part. Students are encouraged to solve a task during the class that follows the homework. The homework is discussed at the beginning of the following class. The Exams is splitted into two parts: theory and practice. 1/3rd of the score is theory 2/3 is practice.
Grading
Andrew graduated from Siberian Federal University and obtained the Master of Science degree in Physics in 2021.
The scientific interests are in biophysics, medicine, and modelling of real biology features in-silico. The master article is devoted to the quantum modelling of an Endothelial Growth Factor Receptor`s ligand as a target for positron emission tomography. Andrew is an awardee of a students olympiad and an active member of a math book translation team.
See full profileApply for this course
Linear Algebra 2
by Andrey Kechin
Total hours
45 Hours
Dates
Sep 07 - Sep 25, 2026
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
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Schedule your Harbour.Space interview
If successful, get ready to join us on campus
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