||On official office hours and by appointment
||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)
- 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.
- Vector spaces. Definition. Examples. Subspaces. Linear Summs of subspaces. Linear dependence and independence. Basis vectors.
- Vector spaces of finite dimension. Linear dependence. Definition of finite dimensionality. Basis. Dimension. Direct sum and complement. Isomorphism.
- 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.
- Polynoms of lin. operator. Minimal polynoms. Eigenvalues and eigenvectors (spectra of operators).
- Bakić, Linearna algebre, Školska knjiga, Zagreb, 2008.
- D. Butković, Predavanja iz linearne algebre, Odjel za matematiku, 2010.
- S. Kurepa, Konačno dimenzionalni vektorski prostori i primjene, Liber, Zagreb, 1992.
- S. Kurepa, Uvod u linearnu algebru, Vektori – matrice – grupe, Školska knjiga, Zagreb, 1978.
- K. Horvatić, Linearna algebra, 9. izdanje, Tehnička knjiga, Zagreb, 2003.
- S. Lang, Introduction to Linear Algebra, Springer – Verlag, 1980.
- S. Lang, Linear Algebra, Springer – Verlag, 2004.
- G. Strang, Introduction to Linear Algebra, Cambridge Press, 1998.
||Lectures, Auditorium Exercises, Consultations
||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.
|Quality control and successfulness follow up
||An anonymous questionnaire