Prerequisite/Recommended prerequisite for participation in the module

Content, progress and pedagogy of the module

Learning objectives

Knowledge

• Vectors, matrices and systems of linear equations
• Connections between solution of systems of linear equations, associated matrices and operations on those
• Linear independence and dimension. Eigenvalues and eigenvectors
• The connection between properties of a matrix and of the echelon form of it
• The connection between a vector space of dimension n and Rⁿ
• Orthogonality and orthonormal bases

Skills

• Matrix-vector product, product and sum of matrices. Row operations. Gauss elimination.
• Eigenvalues and eigenspaces.
• Solution of a system of linear equations on vector form.
• Bases of subspaces associated with a matrice.
• Given a basis for a vector space finding coordinates for vectors and the matrix of a linear map.
• Gram Schmidt, projection on a subspace, projection matrices. Coordinates for a vector wrt. an orthonormal basis.

Competences

Can apply methods and concepts from linear algebra, including vector spaces and orthonormal bases to given problems relevant to the study programme.

Type of instruction

Lectures, exercises, videos, quiz, digitalised self-study, workshops on calculus problems relevant to the study programme.

Extent and expected workload

Since it is a 5 ECTS course, the work load is expected to be 137,5 hours for the student.

Exam

Exams