精品文档---下载后可任意编辑摘要根据矩阵乘法的定义,我们知道要计算矩阵的乘积 AB,就要求矩阵 A 的列数和矩阵 B 的行数相等,否则乘积 AB 是没有意义的。那是不是两个矩阵不满足这个条件就不能计算它们的乘积呢?本文将介绍矩阵的一种特别乘积A⊗B,它对矩阵的行数和列数的并没有具体的要求,它叫做矩阵的 Kronecker 积(也叫直积或张量积)。 本文将从矩阵的 Kronecker 积的定义出发,对矩阵的 Kronecker 积进行介绍和必要的说明。之后,对 Kronecker 积的运算规律,可逆性,秩,特征值,特征向量等性质进行了具体的探究,得出结论并加以证明。此外,还对矩阵的拉直以及矩阵的拉直的性质进行了说明和必要的证明。 矩阵的 Kronecker 积是一种非常重要的矩阵乘积,它应用很广,理论方面在诸如矩阵方程的求解,矩阵微分方程的求解等矩阵理论的讨论中有着广泛的应用,实际应用方面在诸如图像处理,信息处理等方面也起到重要的作用。本文讨论矩阵的 Kronecker 积的性质之后还会具体介绍它在矩阵方程中的一些应用。关键词:矩阵;Kronecker 积;矩阵的拉直;矩阵方程;矩阵微分方程Properties and Applications of matrix Kronecker productAbstractAccording to the definition of matrix multiplication, we know that to calculate the matrix product AB, requires the number of columns of the matrix A and matrix B is equal to the number of rows, otherwise the product AB makes no sense.That is not two matrices not satisfy this condition will not be able to calculate their product do?This article will describe a special matrix product A⊗B, the number of rows and columns of a matrix and its no specific requirements, it is called the matrix Kronecker product (also called direct product or tensor product).This paper will define the matrix Kronecker product of view, the Kronecker product matrix are introduced and the necessary instructions. Thereafter, the operation rules Kronecker product, the nature of reversibility, rank,eigenvalues, eigenvectors, etc. specific inquiry, draw conclusions and to prove it...