Course title Linear algebra 1
Code M103
Status Lectures(30), Seminars(0) Exercises (30)
Level Basic course
Year 1. Semester 2.
ECTS 6 ECTS credits
Lecturer Ivana Kuzmanović Ivičić, Assistant Professor
Course objective Introduction to basic concepts and problems of linear algebra.
Prerequisites Geometry of plane and space
Learning outcomes: After successfully completed course, students will be able to:

  1. describe the structure and give examples of vector space;
  2. explain the concepts of linear dependence and independence;
  3. solve the task of determining the base and/or dimension of a vector space;
  4. use the matrix operations;
  5. examine the regularity of the square matrix;
  6. describe the necessary and sufficient conditions for the solvability of the system of linear equations;
  7. identify and apply different ways of solving linear systems;
  8. check the linearity of the operator;
  9. explain the concepts of rank and nullity of linear operators;
  10. determine the matrix form of a linear operator;
  11. express definition of eigenvalues and eigenvectors;
  12. describe the finding of the characteristic and the minimal polynomial of a linear operator;
  13. specify the definition and examples of inner product;
  14. implement the Gram-Schmidt orthogonalization process
Teaching activity ECTS Learning outcome Students activity Methods of evaluation Points
min max
Class attendance  0,4  1., 2., 6., 9., 11., 13., Class attendance  Evidence list  No points given
Knowledge test (preliminary exam) 3,3 3., 4., 5., 7., 8., 10., 12., 14. Preparation for written examination. Written  preliminary exam  30  100
Final exam  2,3  1. – 14. Repetition of teaching materials. Oral exam (and written exam). No points given
Total 6
Consultations On official office hours and by appointment
Gained competencies Students are becoming familiar with basic knowledge of linear algebra and competence in their application, such as mastery of basic methods of matrix and vector operations, solving systems of linear equations, application of orthogonalization process.
Content (Course curriculum)
  1. Systems of linear equations. Concept of matrices and operation with them – Mm,n(F). space. Diagonal, identity, transpose hermite-conugate matrices. Trace and determinante of matrices. Product of matrices. Nonsingular matrices. Inverse matrices.
  2. Vector spaces. Definition. Examples. Subspaces. Linear Summs of subspaces. Linear dependence and independence. Basis vectors.
  3. Vector spaces of finite dimension. Linear dependence. Definition of finite dimensionality. Basis. Dimension. Direct sum and complement. Isomorphism.
  4. Linear operators. Definition. Theorem about rank and nullity. Operations with operators. Correspondence matrices – operators. Characterisation of an isomorphism with a matrix regularity. Connection between matrices of same operator for different basis.
  5. Polynoms of lin. operator. Minimal polynoms. Eigenvalues and eigenvectors (spectra of operators).
Recommended reading
  1. Bakić, Linearna algebre, Školska knjiga, Zagreb, 2008.
  2. D. Butković, Predavanja iz linearne algebre, Odjel za matematiku, 2010.
Additional reading
  1. S. Kurepa, Konačno dimenzionalni vektorski prostori i primjene, Liber, Zagreb, 1992.
  2. S. Kurepa, Uvod u linearnu algebru, Vektori – matrice – grupe, Školska knjiga, Zagreb, 1978.
  3. K. Horvatić, Linearna algebra, 9. izdanje, Tehnička knjiga, Zagreb, 2003.
  4. S. Lang, Introduction to Linear Algebra, Springer – Verlag, 1980.
  5. S. Lang, Linear Algebra, Springer – Verlag, 2004.
  6. G. Strang, Introduction to Linear Algebra, Cambridge Press, 1998.
Instructional methods Lectures, Auditorium Exercises, Consultations
Exam formats The exam consists of oral and written parts of exam. The students can go in for an exam after attending all lectures and after doing all exercises. During one semester there is a possibility for the students to go in for 2 preliminary exams; these exams can replace the written part of the exam.
Language Croatian
Quality control and successfulness follow up An anonymous questionnaire
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