Teaching Research on Eigenvalues and Eigenvectors Based on the Fibonacci Number Sequence

DOI: https://doi.org/10.62517/jnse.202517302

Author(s)

Tao Chen*, Chao Zhang

Affiliation(s)

Department of Basic Courses, Nanjing Tech University Pujiang Institute, Nanjing, Jiangsu, China *Corresponding Author

Abstract

Eigenvalues and eigenvectors are important concepts in linear algebra and have significant applications in artificial intelligence, big data analysis, and image processing. Most current textbooks introduce eigenvalues and eigenvectors directly from the perspective of mathematical definitions, which makes them difficult for beginners to understand. The difficulty in teaching eigenvalues and eigenvectors lies in making highly abstract mathematical concepts concrete and helping students understand their essence. To achieve the above objectives, this paper attempts to use the Fibonacci sequence, which is familiar to students, as an introductory example. It constructs a system of linear equations using the Fibonacci recurrence formula and applies linear algebra to study the Fibonacci sequence. With the goal of calculating the general term of the Fibonacci sequence, we naturally introduce the concepts of eigenvalues and eigenvectors, as well as the calculation methods for eigenvalues and eigenvectors. While solving problems, students acquire new knowledge. They understand the Fibonacci sequence from the perspective of linear algebra and deepen their comprehension of the concepts of eigenvalues and eigenvectors, as well as their geometric meanings.

Keywords

Eigenvalues; Eigenvectors; Geometric Meanings; Fibonacci Sequence.

References

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