English

Linear algebra and matrices I and II

Lecturer: Johanna Rämö, email: firstname.surname 'at' helsinki.fi

These courses are taught in Finnish. The course assignments, course material and lectures are all in Finnish. However, the exams are provided in English if needed. If you would like to take the exam in English, please contact the lecturer.

Literature

David Poole's book "Linear Algebra: A Modern Introduction" covers well the topics of both courses. If you wish to have a look at the Finnish course material, it can be found under the title "Kurssimateriaali" on the Finnish website.

Topics

The courses cover the following topics. The numbers after each topic show, where the topic can be found in David Poole's book (second edition).

Linear algebra and matrices I

• Vectors of the vector space R ⁿ (1.1)
• Lines and planes (1.3)
• Systems of linear equations (2.1-2.2)
• Spanning sets (2.3)
• Linear independence (2.3)
• Basis (3.5)
• Matrices (3.0-3.3)
• Determinants (4.2)
• Dot product (1.2)
• Cross product (1.3 and Exploration after section 4.2)

Linear algebra and matrices II

• Vector spaces (6.1)
• Subspaces (6.1)
• Linear independence and basis (6.2)
• Linear transformations (6.4-6.6)
• Eigenvalues (4.3-4.4)
• Inner product spaces (7.1)
• Orthogonality (5.1-5.3)

Coursework

Even though the problem sheets are in Finnish, you can probably understand many of the questions. The problem sheets can be found under the title "Harjoitustehtävät" on the Finnish Website.