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.
Determinant.
Classical adjoint and inverse of a matrix, Cramer's rule.
Real and complex vector spaces.
Linear independancy, basis and dimension.
Linear transformations.
Matrices of linear transformations.
Rank and change of basis.
Characteristic polynomial, eigenvalues, eigenvectors.
Cayley-Hamilton theorem, minimal polynomial.
Diagonalization, Schur theorem.
Spectral decomposition , functions of matrices.
Scalar product vector spaces.
Orthonormal basis, Gram-Schmidt orthogonalization.
Linear functionals, adjoint transformation.
Self-adjoint transformations, symmetric and hermitian matrices.
Normal, orthogonal and unitary matrices.
Positive definite matrices.
Quadratic forms, Sylvester theorem.
Second order curves and surfaces.
Linear algebra
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.
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.
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.
Lectures, exercises, homeworks, consultations
4 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Tomaž Košir:
BERNIK, Janez, DRNOVŠEK, Roman, KOKOL-BUKOVŠEK, Damjana, KOŠIR, Tomaž, OMLADIČ, Matjaž, RADJAVI, Heydar. On semitransitive jordan algebras of matrices. Journal of algebra and its applications, ISSN 0219-4988, 2011, vol. 10, iss. 2, str. 319-333. [COBISS-SI-ID 15908697]
KOŠIR, Tomaž, OBLAK, Polona. On pairs of commuting nilpotent matrices. Transformation groups, ISSN 1083-4362, 2009, vol. 14, no. 1, str. 175-182. [COBISS-SI-ID 15077977]
BERNIK, Janez, DRNOVŠEK, Roman, KOŠIR, Tomaž, LIVSHITS, Leo, MASTNAK, Mitja, OMLADIČ, Matjaž, RADJAVI, Heydar. Approximate permutability of traces on semigroups of matrices. Operators and matrices, ISSN 1846-3886, 2007, vol. 1, no. 4, str. 455-467. [COBISS-SI-ID 14492761]
Boris Lavrič:
LAVRIČ, Boris. The isometries of certain maximum norms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2005, vol. 405, str. 249-263. [COBISS-SI-ID 13679961]
LAVRIČ, Boris. The isometries and the G-invariance of certain seminorms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2003, vol. 374, str. 31-40. [COBISS-SI-ID 12751193]
LAVRIČ, Boris. Monotonicity properties of certain classes of norms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 1997, let. 259, str. 237-250. [COBISS-SI-ID 7388761]
