Бакалавриат
2025/2026
Линейная алгебра
Статус:
Курс обязательный (Международная программа по экономике и финансам)
Кто читает:
Международный институт экономики и финансов
Где читается:
Международный институт экономики и финансов
Когда читается:
2-й курс, 1 семестр
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
3
Контактные часы:
64
Course Syllabus
Abstract
Pre-requisites: There are no formal prerequisite courses for Linear Algebra, however some concepts from Calculus and Statistics will be used as illustrations. Therefore, Linear Algebra is recommended for the audience that are familiar with these disciplines.
Course description: Linear Algebra is a one-semester (16 weeks) class that is obligatory for the curriculum of the second-year ICEF students. The course was originally designed as an instrumental supplement to the principal quantitative block subjects such as “Methods of optimization”, “Time series analysis”, and “Econometrics”. Currently, it is taught in ICEF as a self-sufficient discipline to deliver basic principles of linear algebra and matrix calculus. The course splits naturally into the following four parts: 1. Problems related to solving systems of linear equations. This part also includes the concept of a linear space, linear independence, base, rank etc. 2. Problems related to matrix algebra, including not only determinants, matrix products, inverse matrices etc. but also abstract algebraic concepts such as groups and fields, and the field of complex numbers. 3. Problems related to linear operators, eigenvectors and eigenvalues etc. and 4. Problems related to quadratic and bilinear forms.
Learning Objectives
- • Students are expected to develop an understanding of basic algebraic concepts such as linear vector space, linear independence, bases, coordinate systems, dimension, matrix product, quadratic forms, linear operators, matrix diagonalization, dot product, Jordan normal form, orthogonality. On the practical side, among other skills, students are expected to be able to solve systems of linear equations, find fundamental systems of solutions, invert matrices, find eigenvalues, diagonalize matrices, compute Jordan normal form, determine definiteness of a quadratic form, find intersection of linear spaces, and do orthogonal projections.
Expected Learning Outcomes
- Be able to solve arbitrary systems of linear equations
- Test linear independence of vectors
- Find bases of linear spaces and coordinates of a vector in a base
- Compute determinants and matrix products
- Find inverse matrices and solve matrix equations
- Evaluate definiteness of quadratic forms
- Operate with complex numbers and solve polynomial equations
- Find eigenvalues and eigenvectors of linear operators
- Diagonalize matrices and compute real and complex Jordan normal forms
- Be able to do orthogonal projections and find orthogonal bases
Course Contents
- Elements of Set Theory
- Systems of Linear Equations
- Linear Spaces
- Fundamental Set of Solutions
- The Determinant
- Matrix Algebra
- Quadratic forms
- Euclidean vector spaces
- Orthogonal Projection
- The Field of Complex Numbers
- Linear Operators
- Diagonalizable linear operators
- Jordan normal form
- Orthogonal and Self-Adjoint Operators
Assessment Elements
- Home Assignments
- Mock exam
- Final ExamIn order to get a passing grade for the course, the student must sit (all parts) of the examination.
