Bachelor
2020/2021
Further Linear Algebra
Type:
Compulsory course (HSE University and University of London Double Degree Programme in Economics)
Area of studies:
Economics
Delivered by:
International College of Economics and Finance
When:
3 year, 1, 2, 4 module
Mode of studies:
distance learning
Instructors:
Kirill Bukin
Language:
English
ECTS credits:
4
Contact hours:
64
Course Syllabus
Abstract
This course is a continuation of Algebra MT1 173 which is taught for the second-year students. It lasts for one (fall) semester. Upon completion of Further Linear Algebra students will have to take the University of London (UoL) exam at the end of the fourth semester of their studies at ICEF.
Learning Objectives
- The discipline is intended to: • 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. Upon completion of Further Linear Algebra students will have to take the University of London (UoL) exam at the end of the sixth semester of their studies at ICEF.
Expected Learning Outcomes
- find appropriate basis made of ordinary and generalized eigenvectors
- 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
- Use theory of operator projections, primarily orthogonal
- Handle left, right inverses, then weak and strong generalized inverses
- Apply classification of matrices and their properties, define spectral decomposition
Course Contents
- Diagonalization, Jordan normal form and differential equations
- Orthogonal diagonalization and its applications
- Complex matrices and vector spaces
- Direct sums and projections
- Generalized inverses
- Inner products and orthogonality
Interim Assessment
- Interim assessment (2 module)this December exam grade will be applied to the final grade in 4th module
- Interim assessment (4 module)0.3 * December exam + 0.15 * home assignments + 0.25 * mock + 0.3 * UoL 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