Undergraduate study programme


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Linear Algebra P101

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 37100

Course groups

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Course lecturers


Course description

Elements of mathematical logic. Vector space V3. Operations on vectors. Linearly dependent and independent vectors. Vector projection. Base of a vector space. Coordinate system. Scalar, vector and triple product. Analytic geometry. Point, line, plane and mutual relations. Matrix and elementary transformations of matrices. Operations with matrices. Vector space of matrices. Determinant and its properties. Calculation of determinant value. Rank of a matrix. Regular matrices. Inverse matrices. Systems of linear equations. Discussion of solutions. Methods for solving systems of equations. n-dimensional vector space. Base and space dimension. Subspaces. Examples of vector space. Linear operator. Representation of a linear operator in a basis. Algebra. Minimum polynomial. Similarity of matrices. Eigenvalues and eigenvectors. Characteristic polynomial. Hamilton-Cayley theorem. Matrix diagonalisation. Scalar product. Norm. Unitary spaces. Orthogonality. Gramm-Schmidt orthogonalisation. Quadratic forms. Curves of second degree. Second degree surfaces.

Knowledge and skills acquired

Students are introduced to linear algebra calculus and algebraic structures fundamental to many other courses. Lectures and exercises will include basic terminology whose usage will be illustrated by various examples and tasks.

Teaching methods

Students are obliged to attend both lectures and exercises.

Student assessment

During the semester students can take several tests which replace the written examination. This ensures continuous assessment of students’ work and knowledge.

Obligatory literature

1. Elezović, N; Aglić, A. Linearna algebra, zbirka zadataka. Zagreb: Element, 2001.

2. Lipschutz, Seymour. Linear algebra, Schaum's outlines, 1991.

3. K.Horvatić, Linearna algebra, PMF Matematički odjel, Zagreb,1995.

Pretraži literaturu

Recommended additional literature

1. S.Kurepa, Uvod u linearnu algebru, Školska knjiga, Zagreb,1990.

2. L.Čaklović, Zbirka zadataka iz linearne algebre, Školska knjiga, Zagreb 1979.

3. R.Galić, Osnive linearne algebre, ETF, Osijek, 1994.

4. N.Elezović, Linearna algebra, Element, Zagreb, 1995

5. N.Bakić, A.Milas, Zbirka zadataka iz linearne algebre, PMF Matematički odjel, Zagreb,1995.

ECTS credits

An ECTS credit value has been added according to calculation of time required for studying and successful course completion.

Examination methods

The final examination consists of the written and the oral part. Students could take the final examination after the completion of lectures and exercises.

Course assessment

Conducting an anonymous questionnaire filled in by students after course completion, an analysis of students' final assessments and their overall success.

Overview of course assesment

Learning outcomes
Upon successful completion of the course, students will be able to:

1. definirati vektorski prostor i izvršiti osnovne računske operacije s vektorima;

2. definirati matrice i izvršiti osnovne računske operacije s matricama;

3. diskutirati o međusobnom odnosu pravca, ravnine i točke u prostoru;

4. definirati linearni operator, odrediti minimalni polinom i dijagonalizirati matricu;

5. riješiti sustav linearnih jednadžbi različitim metodama i diskutirati o rješenjima.

Learning outcomes available only as desktop version    Export to Excel

Prvo unesite postotak evidencije nazočnosti!

Student's activity Workload ECTS (Workload/30) Learning outcomes
Upon successful completion of the course, students will be able to:
Assessment method Points
Lectures, Auditory exercises

Lectures, Auditory exercises Attendance register. Mandatory attendance percentage is:

This percentage defines the minimum workload for the activity. The maximum is defined by the study programme.


Oral exam Workload

Oral exam Assessment of student's answers Min


Σ Activities Σ Workload
Σ Max