First semester (5 ECTS)
Vectors in Rn. Fundamentals of analytic geometry.
Matrices and determinants. Systems of linear equations.
Basic algebraic structures.
Vector spaces, linear independence, bases.
Linear transformations and their matrices.
Second semester (5 ECTS)
Eigenvalues and eigenvectors of matrices.
Diagonalization and Jordan canonical form.
Inner product spaces, orthonormal bases, adjoint of a linear transformation.
Symmetric, normal and orthogonal matrices.
Quadratic forms. Curves and surfaces of degree two.
Linear algebra
2018/2019
Programme:
Interdisciplinary University Study Programme Computer Science and Mathematics
Year:
1 year
Semester:
first and second
Kind:
mandatory
ECTS:
10
Language:
slovenian
Course director:
Prof. Dr. Jakob Cimprič, Assoc. Prof. Dr. Karin Cvetko Vah
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Readings
Učbeniki in zbirke vaj (Textbooks and problem sets)
J. Grasselli, A. Vadnal: Linearna algebra, linearno programiranje, DMFA založništvo, Ljubljana, 1986.
S. I. Grossman, Elementary linear algebra with applications, McGraw-Hill 1994.
E. Kramar, Rešene naloge iz linearne algebre, DMFA, Ljubljana 1994.
M. Dobovišek, D. Kobal, B. Magajna, Naloge iz algebre I, DMFA, Ljubljana, 2000.
S. Lipschutz: Linear Algebra (Schaum's O.S.), McGraw-Hill, New York 1968.
Elektronski viri (Electronic sourses)
Tomaž Košir, Algebra 1, http://www.fmf.uni-lj.si/~kosir/poucevanje/0910/alg1-fm.html
Bojan Orel, Linearna algebra, http://matematika.fri.uni-lj.si/LA/la1.pdf
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
Familiarity with basic notions and algorithms of Linear algebra. Ability to apply the knowledge in mathematics and elsewhere.
Learning and teaching methods
Lectures, tutorials, homework assignments, consultations.
Assessment
Written exam, coursework
Oral exam
Lecturer's references
Jaka Cimprič:
CIMPRIČ, Jaka. Strict positivstellensätze for matrix polynomials with scalar constraints. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2011, vol. 434, iss. 8, str. 1879-1883. [COBISS-SI-ID 15863385]
CIMPRIČ, Jaka. Archimedean operator-theoretic Positivstellensätze. Journal of functional analysis, ISSN 0022-1236, 2011, vol. 260, iss. 10, str. 3132-3145. [COBISS-SI-ID 15997529]
CIMPRIČ, Jaka. Real algebraic geometry for matrices over commutative rings. Journal of algebra, ISSN 0021-8693, 2012, vol. 359, str. 89-103. [COBISS-SI-ID 16315993]
Karin Cvetko Vah:
CVETKO-VAH, Karin, LEECH, Jonathan. Rings whose idempotents form a multiplicative set. Communications in algebra, ISSN 0092-7872, 2012, vol. 40, no. 9, str. 3288-3307. [COBISS-SI-ID 16432729]
CVETKO-VAH, Karin. On strongly symmetric skew lattices. Algebra universalis, ISSN 0002-5240, 2011, vol. 66, no. 1-2, str. 99-113. [COBISS-SI-ID 16219993]
CVETKO-VAH, Karin. Internal decompositions of skew lattices. Communications in algebra, ISSN 0092-7872, 2007, vol. 35, no. 1, str. 243-247. [COBISS-SI-ID 14223193]
