与方阵A相关矩阵的特征值及特征向量

Eigenvalue and Eigenvector of Some Related Matrices with Square Matrix A

文章由方阵A的特征值及特征向量推导出与其相关矩阵kA、Am、aA+bE、A*、A-1(k、a、b为常数,m∈N+)的特征值及特征向量,并对其应用进行了探究。

This paper discusses the relations between the eigenvalues and eigenvectors of a square matrix and its related matrices,such as inverse matrix,adjoint matrix,and so on.The conclusions are that the latter′s eigenvalues and eigenvectors can be derived from those of the former.Then some examples are demonstrated how to use these conclusions.