Course code

MLM6523.DT

old course code

Course title in Estonian

Algebra II

Course title in English

Algebra II

ECTS credits

4.0

Assessment form

Examination

lecturer of 2023/2024 Spring semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

lecturer of 2024/2025 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

To get acquainted with the terms connected with linear spaces and linear transformations of linear spaces.

Brief description of the course

The main topics of the course are: Linear transformations and isomorphisms of linear spaces. Matrix similarity. Characteristic polynomial of a matrix. Eigenvectors, eigenvalues and the canonical basis of a linear transformation of linear spaces. Jordan matrix. Matrix of a linear transformation and its Jordan canonical form. Euclidean (linear) space. Orthogonal and symmetric matrices. Orthogonal and symmetric transformations. Linear, bilinear and quadratic functionals. Linear, bilinear and quadratic forms. Canonical form of a quadratic form. Reduction of a quadratic form to its canonical form.

Learning outcomes in the course

Upon completing the course the student:
- is familiar with the basic notions connected with linear spaces and their linear transformations;.
- is capable to solve exercises connected with linear spaces.

Teacher

Mart Abel

Prerequisite course 1

Algebra I (MLM6522.DT)

The course is a prerequisite

Study programmes containing that course

Mathematics, Mathematical Economics and Data Analysis (MLMB/24.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/23.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/20.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/19.DT)
Mathematics, Mathematical Economics and Data Analysis (MLMB/18.DT)