Bachelor 2025/2026

Further Linear Algebra

Type: Compulsory course (International Programme in Economics and Finance)

Area of studies: Economics

Delivered by: International College of Economics and Finance

Where: International College of Economics and Finance

When: 3 year, 1, 2 module

Mode of studies: offline

Open to: students of one campus

Instructors: Kirill Bukin

Language: English

ECTS credits: 4

Course Syllabus

Abstract

This course is a continuation of Mathematical Methods for Economists which is taught for the second-year students. It lasts for one (fall) semester.

Learning Objectives

• Enable students to acquire further skills in the techniques of linear algebra,
• Prepare students for further courses in mathematics and related subjects like econometrics and actuarial science.

Expected Learning Outcomes

• find appropriate basis made of ordinary and generalized eigenvectors
• Apply classification of matrices and their properties, define spectral decomposition
• Apply concepts such as Gram-Schmidt process, orthogonality of vectors, orthonormal basis
• Apply techniques of diagonalization of symmetric matrices to classification of conic sections, quadratic forms classification
• Handle left, right inverses, then weak and strong generalized inverses
• Use theory of operator projections, primarily orthogonal

Course Contents

• Diagonalization, Jordan normal form and differential equations
• Inner products and orthogonality
• Orthogonal diagonalization and its applications
• Complex matrices and vector spaces
• Direct sums and projections
• Generalized inverses

Assessment Elements

• Home assignment 1
• mock at the end of module 1
• Final exam
  In order to get a passing grade for the course, the student must sit (all parts) of the examination.
• Home assignment 2

Interim Assessment

• 2025/2026 2nd module
  0.55 * Final exam + 0.1 * Home assignment 1 + 0.1 * Home assignment 2 + 0.25 * mock at the end of module 1

Bibliography

Recommended Core Bibliography

• Linear algebra : concepts and methods, Anthony, M., 2012

Recommended Additional Bibliography

• Anton, H. (2014). Elementary Linear Algebra : Applications Version (Vol. 11th edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639248

Authors

• Bukin Kirill Aleksandrovich