Bachelor
2024/2025
Further Linear Algebra
Type:
Compulsory course (International Programme in Economics and Finance)
Area of studies:
Economics
Delivered by:
International College of Economics and Finance
When:
3 year, 1, 2 module
Mode of studies:
offline
Open to:
students of one campus
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 assignments
- Control workset of problems that should be solved in 80 minutes
- Exam
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