克罗内克积的特征向量  

On the Feature Vector of Kronecker Product

作　　者：孙云欢 白红信 Sun Yunhuan;Bai Hongxin(College of Data Science and Software Engineering,Baoding University,Baoding,Hebei 071000,China;Faculty of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]保定学院数据科学与软件工程学院,河北保定071000 [2]北京工业大学理学部,北京100124

出　　处：《保定学院学报》2022年第2期111-115,共5页Journal of Baoding University

摘　　要：基于矩阵理论中特征值、特征向量、相似矩阵等相关知识和克罗内克积的基本运算性质,首先求得两个可对角化矩阵的克罗内克积的特征向量的表示形式,其次用相似矩阵研究二阶和三阶只有一个特征值且不可对角化矩阵的若尔当标准形的克罗内克积的特征向量表示形式,之后用归纳法及相似矩阵的属于同一特征值的特征子空间同构将若尔当标准形的克罗内克积的特征向量的表示形式推广到n阶只有一个特征值的不可对角化矩阵,最后得到两个矩阵的克罗内克积特征向量的表示形式.This dissertation firstly obtains the representation of feature vectors of Kronecker product of two diagonalizable matrices based on therelevant knowledge of eigenvalues,feature vectors andsimilar matrices in matrix theory and the basic operational properties of Kronecker product.And then the similar matrices are used to study the Kronecker product feature vectors representation of the Jordan Standard of the second and third-ordernon-diagonalizable matrices with only one eigenvalue.Then,by induction and isomorphism of the feature subspace belonging to the same eigenvalues of two similar matrices,the representation of feature vectors of the Kronecker product of the Jordan Standard is extended to the non-diagonalizable matrices with only one eigenvalue of order n.Last,the feature vectors representation of the Kronecker product of two general matrices is obtained.

关 键 词：克罗内克积 特征向量 相似矩阵 若尔当标准形 

分 类 号：O151.21[理学—数学]