The usage of stochastic matrices while learning the topic "eigenvalues and eigenvectors of a matrix" in the course of Higher Mathematic
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Date
2024
Authors
Vlasenko, Kateryna
Armash, Tetiana
Kostikov, Alexander
Lovianova, Iryna
Moiseienko, Mykhailo
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Journal ISSN
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Abstract
The article looks into teaching students mathematical modeling during the mastering of the topic \Eigenvalues and eigenvectors of a matrix" in the Linear Algebra. The modeling is based on the usage of matrices built based on Markov chains. The analysis of the researchers' papers shows that the usage of matrices of this type can be implemented while teaching students of different university specialties. The analysis of the prerequisites for the involvement of stochastic matrices in the consideration of students has helped to determine additional concepts and theorems that should be considered while learning \Eigenvalues and eigenvectors of a matrix". The theorem on the presence of stochastic vectors in a stochastic matrix can serve as a formula for systematizing problems that can present applications of eigenvalues and eigenvectors of the matrix in real-life situations. The results of the experiment conducted using the developed system of problems for students of different University specialties show the improvement of skills provided by mastering the topic \Eigenvalues and eigenvectors of a matrix".
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Keywords
teaching students mathematical modeling, Linear Algebra, matrices, stochastic matrices, conference materials
Citation
The usage of stochastic matrices while learning the topic "eigenvalues and eigenvectors of a matrix" in the course of Higher Mathematics / K. V. Vlasenko, T. S. Armash, A. A. Kostikov, I. V. Lovianova, M. V. Moiseienko // Journal of Physics: Conference Series. - 2024. - Vol. 2871(1). - Art. no. 012002. - 14 р. - https://doi.org/10.1088/1742-6596/2871/1/012002