线性代数课程中的特征值与特征向量教学研究

Teaching of Eigenvalue Problems in Linear Algebra

针对特征值与特征向量的抽象性,本文从特征值和特征向量的概念及特征值分解定理出发,通过几何直观演示、出租车的调配及高维数据的降维两个具体实例,并结合MATLAB软件阐明特征值与特征向量的几何直观性和实际应用,以期学生多角度深入理解特征值与特征向量,激发学生的学习兴趣,培养学生运用数学解决实际问题的能力.

Considering the abstract of the eigenvalue and eigenvector,in this paper,first the concept of the eigenvalue and eigenvector and eigenvalue decomposition theorem are presented, then the geometric visualization, the application of the eigenvalue and eigenvector in taxi allocation and data dimension reduction are addressed by MATLAB mathematical software. This paper emphasizes on applying the eigenvalue and eigenvector to solve the practical problems which deepen the understanding of the students about the eigenvalue and eigenvector.