Uma abordagem para o ensino de autovalores e autovetores resgatando conceitos prévios

Abstract

Linear algebra plays a fundamental role, with applications in areas such as mathematics, engineering, and physics. Among its concepts are eigenvalues and eigenvectors, which have applications in quantum mechanics, image processing, vibration analysis, and linear operator theory. In teaching linear algebra, it is observed that although students generally understand the concepts of eigenvalues and eigenvectors, they often face difficulties related to essential prior knowledge concepts. These prior knowledge concepts from high school include determinants, finding roots of a polynomial, and homogeneous linear systems. The difficulties may result from gaps in learning or retention of these contents. To overcome these challenges, it is essential to have materials that integrate and explain these prior concepts clearly and accessibly, facilitating the understanding of more advanced content. This work proposes an approach to teaching eigenvalues and eigenvectors, focusing on the recovery of prior high school concepts, with the aim of improving student understanding and illustrating the relevance of these concepts through a practical application, such as in Civil Engineering in the calculation of principal stresses and principal directions. The research is primarily basic, focusing on presenting theoretical concepts in an objective and exploratory manner using a qualitative approach, which involves literature review for the creation of didactic material that contributes to the teaching of eigenvalues and eigenvectors.