Math205
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. Since 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 applications in the majority of the Natural Sciences (Physics, Chemistry, Electronics, etc.) as well as in some more advanced areas of mathematics (such as Optimization Theory, Control Theory, 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 (these are the courses that may demand this course as a prerequisite).
Learning highlights
- Our main goal is to develop a good understanding of what linear transforms do.
- Based on this understanding, we will learn to analyze the matrix properties such as determinants, eigen values and vectors, SVD decomposition and other matrix factorizations.
- Furthermore, we will touch on advanced topics that emerge from classical Linear Algebra, such as tensors, Hilbert Spaces and Fourier Series.
Course outline
15 classes
Class 1
Rehearsal. Linear transforms and the geometric meaning of linear transforms.
Class 2
Determinants. Properties of Determinants. Permutations and Cofactors
Class 3
Cramer’s rule, Inverse Matrix. Determinant as volume.
Class 4
Eigenvalues and Eigenvectors. Equation for Eigenvectors. Matrix diagonalization
Class 5
Symmetric matrices. Positive and negative definite matrices.
Class 6
Covariance Matrix. Singular Value Decomposition. Properties.
Class 7
Linear Transformation. Matrix of a linear transformation. Rotation Matrix. Change of Basis.
Class 8
Diagonalization and Pseudoinverse. Least Squares solution. Matrix derivatives.
Class 9
Tensors and operations with Tensors. Einstein’s rule. Vectors and co-vectors. Differentiation with tensors.
Class 10
Applications of Linear Algebra in Science. Data Fitting. Tomography. Optimization theory.
Class 11
Hilbert spaces. Generalization of Scalar Product. Fourier Series.
Class 12
Inverse Problems. Truncated SVD. Regularization.
Class 13
Complex Vectors and Matrices. Hermitian and Unary Matrices.
Class 14
Matrix Factorizations.
Class 15
Final exam
Prerequisites
Linear Algebra 1, Calculus (derivatives), Python programming (cycles and if-statements, functions, classes)
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.
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
Jan 11 - Jan 29, 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.