特征值与特征向量在线性代数中的应用

Applications of the Eigenvalues and Eigenvectors in Linear Algebra

对矩阵的特征值与特征向量研究具有一定意义。对矩阵特征值与特征向量在求矩阵的幂、判定矩阵对角化、求解特征值的反问题、判定矩阵合同关系以及判定实二次型的正定性等问题进行系统地归纳与分析,以期对线性代数教学与学习提供参考。

It is of certain significance to study eigenvalues and eigenvectors of matrices.This paper systematically summarizes and analyzes the problems of eigenvalues and eigenvectors of matrices in computing the power of matrices,solving inverse problems of eigenvalues,judging the diagonalization of matrices,and determining the congruent relations of matrices and the positive definiteness of real quadratic forms,which provides references for linear algebra teaching and learning.