Abstract:

The studying of the eigenvalues and eigenvectors is an attractive illustration of the application of the ideas and techniques of linear algebra in our everyday live. The basic algorithms for finding eigenvalues and eigenvectors, are separately quite easy to understand for students. Unfortunately, the application of these techniques is already difficult, and the students have a big problem with solving of the practical examples, in which the eigenvalues and eigenvectors appear. Consequently, the aim of this paper is to show some simple practical applications which are suitable for teaching the theory of the eigenvalues and eigenvectors and call attention to the most common student’s mistakes in solving of these problems. All applications will be solved using the matrices and it will be also accompanied by a Matlab script and if possible, also presented graphically. All presented applications were used in teaching of mathematics especially linear algebra at Faculty of Transport Engineering, University of Pardubice and they can be used as an inspiration for teaching at the other universities with the same or similar focus.

Keywords:

Matrix, eigenvalues, eigenvectors, applied mathematics, Matlab.