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Linear algebra and matrices I and II

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

These courses are taught in Finnish. The course assignments, course material and lectures are all in Finnish. However, you can submit your coursework in English. The exams are provided in English if needed.

  • If you would like to take the course exam in English, please contact the lecturer. The date of the course exam can be found on the Finnish website under the title "Kurssikoe".
  • You can also take the exam in a general examination. The general examination dates can be found on the teaching website of the department under the titles Yleistentit and Kesätentit.


Teaching assistants are available in Ratkomo (3rd floor of Exactum) from Monday to Friday.


David Poole's book "Linear Algebra: A Modern Introduction" covers quite 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.


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). You can use any edition of the book.

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)
  • Eigenvalues and eigenvectors of nxn-matrices, Diagonalization (4.3-4.4)
  • 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)
  • Change of basis (6.3)
  • Linear transformations (6.4-6.6)
  • Eigenvalues of linear transformations (not found in Poole)
  • Inner product spaces (7.1)
  • Orthogonality (5.1-5.3)

Course assignments

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. By completing coursework you can gain bonus points that you can use in the exam. The bonus points are valid for one year.

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