## 矩阵直积的性质及应用

Matrix Properties And Applications of Direct Product
Abstract: In this paper, based on the extensive literature, some properties of the direct product of matrices and prove the properties of the inpidual. According to the definition of matrix direct product, set the feature matrix direct product value and the relationship between the two eigenvalues of matrix, the relationship between the determinant of matrix direct product and primary determinant, the relationship between the original and the rank of matrix direct product of matrix rank the Kronecker product of matrix, solution method gives a class special matrix equation AX+XB=F, and gives a concrete solution by examples.
Key words: Matrix direct product ；Matrix straight；The eigenvalue; Matrix equation

1.矩阵直积的定义及性质3
1.1 矩阵直积.3
1.2 矩阵直积的性质.3
2.矩阵直积在解矩阵方程中的应用9
2.1 矩阵的拉直.9
2.2 线性矩阵方程10
3.结束语.14
4.参考文献.15
5.感谢语.16

文献[1]-[4]在给出了矩阵直积的概念的基础上讨论了相关的一些性质，并对其进行了证明；文献[5]-[6]则对矩阵方程的可解性及解法进行了系统的讨论；文献[7]-[10]则提出了利用矩阵直积由已知正交变换到新的正交变换的几种构造方法。

1. 矩阵直积的定义与性质
1.1 矩阵直积

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，称 为向量 与 的外积.
1.2  矩阵直积的性质

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