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# Applied Linear Algebra

IT-ALI1

2.0

ICT Engineering

## ECTS

5

### Prerequisites

Upper level mathematics equivalent to A-levels.

There is a limit of 40 participants in the course. In the event that more than 40 students select the course, we will select the 40 students based on their grades in MSE1 or other equivalent math courses.

### Main purpose

The purpose of the course is to equip the student with basic knowledge about linear algebra and its applications. This will enable the student to not only understand but also apply linear algebra in solving practical engineering problems. Skills in linear algebra are of high importance when dealing with scientific computing, image processing graphics, robot technology, algorithmics, coding theory, and more. As an example, the founders of Google have cited their course in linear algebra as the backbone of Google’s PageRank feature (i.e. ordering web pages after importance). The course familiarizes students with scalars, vectors, matrices, determinants, operations on vectors and matrices, and systems of linear equations in matrix form. The course also presents applications of matrix theory to linear models, including examples from engineering.

### Knowledge

After successfully completing the course, the student will have gained knowledge about:
• What a vector space is, and
• How a linear representation of such spaces can be analyzed using matrix operations
• Application of linear algebra in engineering

### Skills

After successfully completing the course, the student will be able to:
• Apply techniques and results from linear algebra to solve problems in linear systems, matrices, vector space, orthogonality, eigen vectors, and eigenvalue
• Apply theory to analyze basic theoretic tasks within the below mentioned topics
• Express mathematically correct arguments
• Use mathematical terminology and symbol language

### Competences

After successfully completing the course, the student will have acquired competences in:
• Applying linear algebra to the study of various phenomena in engineering science
• Using matrices to solve concrete problems
• Using vector operations to solve concrete problems
• Applying methods and results from linear algebra in the solution of engineering problems

### Topics

• Systems of linear equations and their solutions
• Matrix algebra
• Determinants
• Vector spaces
• The eigenvalue problems
• Orthogonality
• Singular value decomposition

### Teaching methods and study activities

The course is taught as an intensive 3-week course starting Monday week 32. There are 40 theoretical lessons and 20 exercise lessons, a total of 60 lessons. One lesson is 45 minutes. The total workload is expected to be around 120 hours.

### Resources

David C. Lay, 4. edition: Linear Algebra and its applications
Python

### Examination

The final exam has two parts.

The first part is a Flowlock exam in Wiseflow. The students are allowed to use any notes, books, and/or other written/printed material and will have access to pdf files on their laptop.

The second part is a Wiseflow exam without Flowlock. All supplementary materials and aids are allowed, e.g., using a computer as a reference work. It is not allowed, however, to use AI-tools such as CoPilot, ChatGPT, Bing, etc. as per the general VIA rules. The second part must be completed in the Jupyter Notebook environment and the answers must be submitted in Wiseflow.

The exam has a total duration of 4 hours. The student will not be able to access the second part before the first part is concluded. Each part has an equal weight in the final grade. Communication of any sort is not allowed during the exam and will lead to expulsion of all involved parties from the exam.

Internal assessment.

​The re-exam may be held as an oral examination.

Mark 12:
Awarded to students who have shown excellent comprehension of the above-mentioned knowledge, skills, and competences. A few minor errors and shortfalls are acceptable.

Mark 02:
Awarded to students for the just acceptable level of comprehension of the required knowledge, skills, and competences.

Richard Brooks

### Valid from

8/1/2023 12:00:00 AM

### Keywords

Linear algebra, matrices, vectors