Further Linear Algebra

2019/2020

Учебный год

ENG

Обучение ведется на английском языке

5

Кредиты

Кто читает:

Международный институт экономики и финансов

Статус:

Курс по выбору

Когда читается:

4-й курс, 1, 2 модуль

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

• 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 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
• Inner products and orthogonality
• Orthogonal diagonalization and its applications
• Direct sums and projections
• Generalized inverses
• Complex matrices and vector spaces

Assessment Elements

• home assignments
• Mid-term test
• December exam
• UoL exam
  UoL exam is not counted to overall grade of 4th year students.

Interim Assessment

• Interim assessment (2 module)
  0.25 * home assignments + 0.5 * December exam + 0.25 * Mid-term test

Bibliography

Recommended Core Bibliography

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