Exploration of Teaching Matrix Eigenvalues and Eigenvectors in Linear Algebra
The difficulty of teaching linear algebra lies in combining abstract concepts with geometric meanings,gradually cultivating students'visual cognitive processes.This article uses the mathematical idea of combining numbers and shapes to derive the geometric meaning of eigenvalues and eigenvectors from linear transformations in two-dimensional space;And in response to the difficulty in solving feature polynomials in large-scale problems,this paper introduces the numerical solution of eigenvalues and eigenvectors,and discusses the influence of special matrices on the existence of real eigenvalues and eigenvectors,aiming to help students deepen their understanding of the basic concepts of linear algebra and improve their ability to solve practical problems.
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