# MATH280 Applied Linear Algebra

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#### Showing course contents for the educational year 2021 - 2022 .

Course responsible: Geir Bogfjellmo
ECTS credits: 10
Faculty: Faculty of Science and Technology
Teaching language: EN
(NO=norsk, EN=Engelsk)
Teaching exam periods:
This course starts in Spring parallel. This course has teaching/evaluation in the spring parallel, .
Course frequency: Annually. Minimum 10 students.
First time: Study year 2009-2010
Course contents:
The most important parts of each topic are covered in lectures. Thereafter the students are given exercises on the same topics. The aims of the exercises are for students to understand methods and ideas as well as to be able to apply the subject various subjects to relevant practical problems.
Learning outcome:

Theoretical understanding of the basic methods in applied linear algebra, selected optimization problems and insight in selected practical applications, i.e:

• Numerical aspects associated with solving Linear Equations
• Vector Spaces and Linear Transformations
• Diagonalization and change of Change of Coordinate Basis
• Inner Products, Length, Orthogonality and Inner Product Spaces
• Orthogonal Projections and Least-Squares Problems
• The Gram-Schmidt process and QR-factorization
• The Singular Value Decomposition
• The condition number
• Tikhonov regularization

The practical applications include:

• Constrained Optimization
• Principal component analysis
• Linear Regression (Principal Component Regression, Weighted Least Squares)
• Dynamical Systems
Learning activities:
The teaching is given as lectures (covering both theory and practical problemsolving) by the professor responsible for the course + exercise groups including both theoretical and practical problemsolving.
Teaching support:

Canvas is used for the course.

The students can also contact the teacher responsible for the course at the teacher's office, by telephone or by e-mail.

Syllabus:
Announced at the first lecture.
Prerequisites:
MATH113 or MATH131
Recommended prerequisites:
MATH111, MATH112, basic skills in Python/NumPy or a similar programming language.
Mandatory activity:
No compulsory activities.
Assessment:
Final written exam, 3.5 hours.