Math402
Linear Algebra 2
Faculty
Mikhail Romanov
Senior Machine Learning Engineer, Yandex, Expert
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Linear Algebra is one of the core mathematical fields. In the beginning of the 20th Century, the demand in this area has grown tremendously with the rise of Quantum Mechanics. Since then, it has found numerous applications in the majority of the Natural Sciences (Physics, Chemistry, Electronics, etc.) as well as in Scientific Computing (Optimization Theory, Theory of Control, Machine Learning, Computer Vision, Signal Processing, etc.).
This course is a successor of a Linear Algebra 1 course.
This course is a must-know for areas such as Machine Learning, Optimization Theory, Theory of Control, Deep Learning and Neural Networks (these are the courses that may demand this course as a prerequisite).
Learning highlights
- Analysing the matrices, linear transforms and bilinear forms
- Finding the eigen values and vectors and singular values and vectors
- Matrix decompositions and their properties
- Linear Operators for discrete functions, Hilbert Spaces, Fourier Transforms, Discrete Fourier Transforms
- Tensors (covariant and contravariant) and operations with Tensors
Course outline
15 classes
Session 1
Rehearsal. Linear transforms and the geometric meaning of linear transforms.
Session 2
Seminar: Rehearsal
Session 3
Determinants. Properties of Determinants. Permutations and Cofactors. Cramer’s rule, Inverse Matrix. Determinant as volume.
Session 4
Seminar: Determinants
Session 5
Eigenvalues and Eigenvectors. Equation for Eigenvectors. Matrix diagonalization.
Symmetric matrices. Positive and negative definite matrices.
Session 6
Seminar: Eigenvectors and Eigenvalues
Session 7
Covariance Matrix. Singular Value Decomposition. Properties. Diagonalization and Pseudoinverse.
Session 8
Seminar: SVD
Session 9
Complex Vectors and Matrices. Hermitian and Unary Matrices.
Session 10
Seminar: Complex vectors and matrices
Session 11
Hilbert spaces. Generalization of Scalar Product. Fourier Transform. Discrete Fourier Transform.
Session 12
Seminar: Fourier Transform
Session 13
Linear Transformation. Matrix of a linear transformation. Rotation Matrix. Change of Basis.
Tensors and operations with Tensors. Einstein’s rule. Vectors and co-vectors.
Session 14
Seminar: Tensors.
Applications of linear algebra in Science
Session 15
Final exam
Course materials
Books
Methodology
Our sessions consist of two parts: a lecture session with slides and theoretical materials and a seminar session with problem solving. The seminar sessions will include both math problems and programming tasks.
The knowledge is the amount of problems that you have solved. Thus, I will be marking your homework assignments and practical tasks. Class activity will be rewarded with extra points.
Grading
Mikhail Romanov, PhD, is a deep learning researcher and engineer. His experience includes deep learning for production, scientific computing and research, accompanied by teaching mathematics and machine learning in general.
His academic experience includes teaching courses at MIPT, HSE, Harbour Space Universities and online platforms. As a researcher, he has conducted research at the Technical University of Denmark, Mail.ru, Samsung Research, Quantori, and Yandex. In his research, his main areas of interest are depth estimation, optical flow, optimisation of neural networks, multi-task learning, self-supervised learning, LLMs and diffusion models. He has published papers on tomography, deep learning, scientific computing, computer vision, generative AI, and diffusion models.
See full profileApply for this course
Linear Algebra 2
by Mikhail Romanov
Total hours
45 Hours
Dates
Nov 29 - Dec 17, 2021
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.