Linear Algebra
Data is displayed for the academic year: 2024./2025.
Exercises
Course Description
Matrix calculus, determinants, solving linear systems of equations.
Vector analysis and analytic geometry of space. Vector spaces, linear operators, eigenvalues and eigenvectors, operator diagonalization.
Prerequisites
-
Study Programmes
University undergraduate
[FER3-EN] Computing - study
(1. semester)
[FER3-EN] Electrical Engineering and Information Technology - study
(1. semester)
Learning Outcomes
- describe and apply linear algebra basic concepts and methods
- demonstrate fundamental skills of matrix calculus and solving linear systems of equations
- apply fundamental knowledge of vector analysis and space analytic geometry
- demonstrate basic knowledge of vector spaces and linear operators
- demonstrate an ability to express mathematical ideas and abstract thinking in linear algebra
- demonstrate an ability to basic problem solving and reaching conclusions in linear algebra
- use methods of linear algebra in engineering
Forms of Teaching
Lectures
Lectures are held in two cycles, 4 hours per week
ExercisesExercises are held in two cycles, 4 hours per week
Partial e-learningHomework is accessible on course web-page.
Grading Method
Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|
Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||
Homeworks | 50 % | 0 % | 0 % | 0 % | ||
Attendance | 50 % | 0 % | 0 % | 0 % | ||
Mid Term Exam: Written | 0 % | 50 % | 0 % | |||
Final Exam: Written | 0 % | 50 % | ||||
Exam: Written | 0 % | 100 % |
Comment:
Regular attendance of lectures and doing homework are requirement for taking exam.
Week by Week Schedule
- Matrices; Basic types; Operations with matrices; Inverse matrix; Regular and singular matrices
- Determinants; Basic properties, computation of determinants; Laplace's rule, Elementary transformations, rank of a matrix, linear independence and rank; Characterization of regular matrices
- Elementary transformations, rank of a matrix, linear independence and rank; Characterization of regular matrices, Characterization of regular matrices using determinant; Computation of the inverse matrix
- Gaussian elimination method; Homogeneous and nonhomogeneous systems, Rank of a system and rank of extended matrix
- Rank of a system and rank of extended matrix, Cramer's rule; Comparison of computational complexity of the Gauss and Cramer algorithms
- Operations with vectors; Linear dependence and independence in V^2 and V^3; Bases in V^2 and V^3; Canonical base; Vectors in coordinate systems, Dot product; Norm, ortogonality; Vector and scalar projections of one vector on another
- Cross product of two vectors and mixed product of three vectors, Radius-vector; Coordinates of the midpoint of a segment and of the barycenter of a triangle; Convex combinations of vectors; Convex hull; Convex set
- Midterm exam
- Equations of plane; Mutual position of two planes; Distance between a point and a plane
- Line, parametric and canonical equations; Mutual position of a line and a plane
- Vector spaces and their subspaces; Linear hull (span); The space R^n, Linear independence and dependence; Basis and dimension
- Coordinate system; Basis change; Transition matrix, Inner product; Inner product space; Orthogonal basis; Fourier coefficient; Orthogonal projection; Normed vector space
- Linear operators and their matrix representation; Basis change; Similar matrices, Examples of linear operators in V^2 and V^3; Linear functional; Hyperspace, half-space
- Eigenvalues and eigenvectors; Eigenspaces; Characteristic polynomial; Hamilton-Cayley's theorem, Schur's theorem; Matrix functions; Spectral mapping theorem
- Final exam
Literature
Neven Elezović (2016.), Linearna algebra, Element, Zagreb
N. Elezović, A. Aglić Aljinović (2006.), Linearna algebra: zbirka zadataka, Element, Zagreb
Damir Bakić (2008.), Linearna algebra, Školska knjiga, Zagreb
David S. Watkins (2002.), Fundamentals of Matrix Computations, Wiley
General
ID 209622
Winter semester
5 ECTS
L0 English Level
L2 e-Learning
60 Lectures
0 Seminar
15 Exercises
0 Laboratory exercises
0 Project laboratory
0 Physical education excercises
Grading System
85 Excellent
70 Very Good
55 Good
45 Sufficient