Study program
First cycle study programme in mathematics (Bachelor
level)
1st cycle
Study level
Course title
Linear algebra II
Course code
MAT01-011
Language of instruction
English
Course objective. Introduction to basic ideas and problems
of linear algebra.
Prerequisites. Linear algebra I.
Course contents.
Course description
Form of teaching
Form of assessment
I. Determinants
1. The Pivot Formula. Definition of determinants as a
linear function of rows separately. Elementary properties.
2. The Permutation or Big Formula. The cofactor formula.
The Cramer’s rule. The Binet – Cauchy theorem.
II. Linear Operators
3. Change of Bases. Similar matrices.
4. Adjoint Operators. Dot products in new bases. The four
subspaces of an operator.
5. Eigenvalues and Eigenvectors. The invariant subspaces.
Diagonalising a matrix. Jordan matrices.
6. Symmetric Matrices. Positive definite and semidefinite
matrices. Quadratic forms.
7. Complex Eigenvalues and Eigenvectors. Orthonormal
matrices. Complex dot product.
8. Unitary and Hermitian Matrices. Diagonalizing a
Hermition Matrix.
III. Matrix Polynomials
9. The Characteristic Equation and Characteristic
Polynomial. The Hamilton – Cayley theorem.
10. The Minimal Polynomial. Definition and
properties. Applications.
consultative teaching
Knowledge assessment consists of three parts:
1. Points obtained through three preliminary tests
held during the semester
2. Points obtained at the final examination
3. Oral part of the examination
Number of ECTS
6
Class hours per week
2+2+0
Minimum number of
students
Period of realization
winter semester
Lecturer
Darija Marković, Assistant Professor