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Mälardalen University, School of Education, Culture and Communication

Objectives

The course provides broad knowledge of applications of matrices and of the essential tools of matrix analysis in various areas of engineering and natural sciences. The basic concepts and methods of importance for further study is explained with practical examples from finance, economics, statistics, discrete mathematics and related models from energy, environment and resource optimization, systems analysis, automatic control, computer science and information technology. In addition to training in logical and geometric thinking and the modeling and computing with matrices of particular importance for applications, as well as the capacity for independent analysis and solution of mathematical problems and models is trained.

Learning objectives

After completing the course, students should be able to
- describe the basic properties of non-negative and stochastic matrices, their connection with graphs and Markov chains and applications in economics, resource optimization, information technology, linear and dynamic programming, decision making, game theory and systems analysis.
- calculate the matrix, canonical forms, functions of matrices and solutions of matrix equations and apply them in studies of system stability and in energy engineering.
- describe different types of matrix and vector norms, and calculate or estimate those with and without computer.
- explore and analyse iterative algorithms for calculating eigenvalues and eigenvectors for various types of matrices with and without computer.
- describe the properties of quadratic forms, projections, spectral theory and their use in quadratic optimization and variational principles and applications in statistics, finance and automatic control.
- analyse the matrix computations in geometrical terms of linear spaces, linear transformations and symmetries.
- explain the concepts within content of the course in a way that is appropriate for the recipient's prior knowledge, and describe a handful of applications.
- describe in detail a freely chosen application area of matrix analysis.

Course content

Non-negative and stochastic matrices; matrix factorisations, canonical forms, matrix polynomials and matrix functions, matrix equations and system stability, spectral theory, projections, norms of matrices and vectors, scalar, singular values, quadratic forms, quadratic optimization and variational principles; iterative algorithms for matrices; matrix computations in terms of linear transformations and symmetries; applications of matrix analysis in engineering and natural sciences.

Teaching methods

Lectures, and classes with work individually and in group.

Prerequisites

At least 120 credits totally from these areas: technical, natural sciences, business administration or economics where Calculus II 7,5 credits and Algebra 7,5 credits or equivalent is included and a TOEFL test result, minimum score 173 (CBT), 500 (PBT) or 61 (iBT) or an IELTS test result with an overall band score of minimum 5,0 and no band score below 4,5. The English test is COMPULSORY for all applicants except citizens of Australia, Canada, Ireland, New Zealand, United Kingdom and USA.

Examination

Rules and regulations for examinations in undergraduate education at Mälardalen University

Marks

Pass (G) or Pass with distinction (VG).

Workload

1.5 credits correspond to approximately 40 hours per week. The individual labor input, i.e. hours per week, may however vary depending on previous knowledge or other circumstances.

Environmental aspects

No specific environmental aspects are included in this course.

Literature

The literature can be found in the university's digital archive.