# Advanced Linear Algebra

## Code

ME-ALA1

## Version

1.0

## Offered by

Mechanical Engineering

## ECTS

5### Prerequisites

ME/MAT-MAT2

### Main purpose

To give a better understanding of linear algebra with a focus on topics and applications relevant for engineering.

### Knowledge

After completing the course, the student can:

- Define a vector space and explain concepts like basis and dimension
- Define linear transformations and list important examples
- Recognize eigenvalue problems

### Skills

After completing the course, the student can:

- Solve systems of linear equations and account for the structure of the solution set
- Manipulate vectors and matrices
- Solve eigenvalue problems and perform singular value decomposition
- Write computer code to manipulate data in vector and matrix form

### Competences

After having completed the course, the student can:

- Analyse physical systems using linear algebra tools and concepts
- Implement simple numerical algorithms
- Understand technical texts using the language of linear algebra

### Topics

### Teaching methods and study activities

The course duration is approximately 12 weeks with 4 lessons per week. The expected work load for the student is approximately 138 hours.

The teaching consists of lectures and problem solving in class. The student must prepare for classes by reading and solving problems. Some problems will involve write computer code. A selection of problems from throughout the semester will constitute the course assignment.

The teaching consists of lectures and problem solving in class. The student must prepare for classes by reading and solving problems. Some problems will involve write computer code. A selection of problems from throughout the semester will constitute the course assignment.

### Resources

David C. Lay, Linear Algebra and its Applications, Global Edition, latest edition (Pearson)

The student will have the option of using either Matlab (VIA licens) or Python (free)

### Evaluation

### Examination

Prerequisites for exam:

The course assignment must be handed in before a deadline set by the teacher. If the assignment is not handed in, the student has used one exam attempt and a new deadline will be set.

The course assignment must be handed in before a deadline set by the teacher. If the assignment is not handed in, the student has used one exam attempt and a new deadline will be set.

Exam type:

Individual oral exam based on the course assignment. Duration is approximately 20 minutes. There is no preparation time. Internal co-examiner.

Individual oral exam based on the course assignment. Duration is approximately 20 minutes. There is no preparation time. Internal co-examiner.

Tools allowed:

None

None

Re-exam:

As the ordinary exam. The student will have the opportunity to hand in a new solution of the same course assignment.

As the ordinary exam. The student will have the opportunity to hand in a new solution of the same course assignment.

### Grading criteria

Grading based on the Danish 7-point scale.

### Additional information

### Responsible

Uffe Vestergaard Poulsen

### Valid from

01-08-2023 00:00:00

### Course type

7. semester

Elective for Mechanical Engineering

### Keywords

- Vector spaces - Systems of linear equations and their solutions - Determinants - Linear transformations - Eigenvalue problems - Orthogonality and rotations - Singular value decomposition