Linear algebra

2021/2022
Programme:
Applied Physisc, First Cycle
Year:
year
Semester:
first
Kind:
mandatory
ECTS:
6
Language:
slovenian
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
3
Lab
0
Prerequisites

Enrollment into the program

Content (Syllabus outline)

Plane vectors and three-dimensional space vectors.
Dot product, cross product, box product.
Lines and planes, distances between points, lines and planes.
Matrices, algebraic operations with matrices.
Elementary transformations, row echelon form.
Systems of linear equations, Gauss elimination.
Inverse of a matrix.
Real and complex vector spaces.
Linear independancy, basis and dimension.
Linear transformations.
Matrices of linear transformations.
Rank and change of basis.
Diagonalization.
Determinant.
Characteristic polynomial, eigenvalues, eigenvectors.
Scalar product in euclidean space.
Real symmetric matrices.

Readings

J. Grasselli, A. Vadnal: Linearna algebra, linearno programiranje, DMFA založništvo, Ljubljana, 1986.
T. Košir: Zapiski s predavanj iz Linearne algebre (spletna učilnica)
E. Kramar: Rešene naloge iz linearne algebre, DMFA založništvo, Ljubljana, 1994.
S. I. Grossman: Elementary linear algebra with applications, McGraw-Hill, 1994.
D. C. Lay: Linear algebra and its applications, Reading: Addison-Wesley, 1994.
The linear algebra problem solver : a complete solution guide to any textbook. Piscataway: Research and Education Association, 1993.

Objectives and competences

Students get familiar with the basic concepts of linear algebra, necessary for further study: basics of two and three-dimensional euclidean geometry, matrix algebra, solving systems of linear equations, calculating with polynomials and basic elements of abstract algebra. They learn a mathematical way of thinking and achieve practical and working knowledge from the field of linear algebra.

Intended learning outcomes

Knowledge and understanding:
Knowledge and understanding of the basic concepts and methods of linear algebra. Application of the achieved knowledge.

Application:
Linear algebra is one of the fundamental subjects in the study of natural, technical, social and almost all other science fields.

Reflection:
Integrating theoretical and practical procedures for solving basic practical problems.

Transferable skills:
Mathematically correct formulation of problems, the choice of appropriate methods, capability of acurate solving of problems and analysis of obtained results.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

[1] J. Bernik, R. Drnovšek, D. Kokol-Bukovšek, T. Košir, M. Omladič, and H. Radjavi: On semitransitive Jordan algebras of matrices. J. Algebra Appl. 10 (2011), no. 2, 319-333.
[2] T. Košir, P. Oblak: On pairs of commuting nilpotent matrices. Transform. Groups 14 (2009), 175–182.
[3] J. Bernik, R. Drnovšek, T. Košir, L. Livshits, M. Mastnak, M. Omladič, H. Radjavi: Approximate permutability of traces on semigroups of matrices, Operators & Matrices 1 (2007), no. 4, 455–467.
[4] B. Lavrič: The isometries of certain maximum norms, Linear Algebra Appl. 405 (2005), 249-263.
[5] B. Lavrič: The isometries and the G-invariance of certain seminorms, Linear Algebra Appl. 374 (2003), 31-40.
[6] B. Lavrič: Monotonicity properties of certain classes of norms, Linear Algebra Appl. 259 (1997), 237-250.