矩阵乘积的特征值与特征向量

矩阵乘积的特征值与特征向量

摘 要： 特征值与特征向量是代数研究的中心问题之1,是两个密切相关的概念．在理论和实际应用中,特征值与特征向量都有举足轻重的地位．本文主要是对矩阵乘积特征值与特征向量的性质进行讨论,给出了矩阵乘积 与 有相等的特征值与特征向量的条件．对各种条件给出了多种不同的证明过程,且进行了1定的推广及应用．

关键字： 矩阵、乘积、特征值、特征向量．

The Eigenvalue and Eigenvector of Matrix Product

Abstract: The eigenvalue and eigenvector are consanguineous conception,one of zhe centre problem of algebra disquisition . Playing a decisive role in theory and actual application .The relationship between the eigenvalue and eigenvector is discussed.The condition of matrices AB and BA having equal eigenvalue and eigenvector is given.Given diffirent kinds of provement to these condition, making more widespread and application.

Keywords: matrix; product ;eigenvalue ; eigenvector．