浅谈方阵及其转置矩阵的特征向量之间的关系  

On the Relationship between the Eigenvectors of Square Matrix and Its Transpose Matrix

作　　者：李东伟 宁荣健[1] LI Dongwei;NING Rongjian(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第5期55-60,共6页College Mathematics

基　　金：合肥工业大学青年教师教学研究项目(JYQN2223);安徽省自然科学基金(JZ2019AKZR0223)。

摘　　要：刻画了方阵和其转置矩阵的特征向量的关系.一方面,当方阵是可相似对角化时,给出了利用方阵特征向量求其转置矩阵的特征向量的方法;另一方面,从约当标准型的角度给出了方阵及其转置矩阵的特征向量的求解方法,这些结果丰富了特征值和特征向量的理论和方法.The relationship between the eigenvectors of the square matrix and its transpose matrix is given.On the one hand,when the square matrix is similarly diagonalizable,a method for finding the eigenvectors of the transpose matrix by using the eigenvectors of the square matrix is given.On the other hand,from the view of Jordan canonical form,the method of solving the eigenvectors of the square matrix and its transposed matrix is given.These results enrich the theory and method of eigenvalues and eigenvectors.

关 键 词：转置矩阵 特征值 特征向量 

分 类 号：O151.21[理学—数学]