关于Kronecker积的特征值与奇异值研究

Study on Eigenvalue and Singular Value of Kronecker Product

Kronecker积既是一种重要的矩阵乘积又是解矩阵方程的重要工具。利用奇异值分解以及特征值和奇异值的基本性质,研究Kronecker积下的特征值和奇异值问题,获得了Kronecker积AB和BA的行列式和迹的关系,Kronecker和的特征值及一个Hadamard积的不等式。

Abstraet：Kronecker product is an important matrix product and useful tool in solving matrix equa- tions. According to the basic properties of eigenvalue and singular value as well as the singular value decomposition, we study eigenvalue and singular value of Kronecker product, Firstly, the relations of the determinant and trace of A B and B A are obtained. Secondly, the eigenvalue of Kronecker sum and a Hadamard inequality are given. Key words：eigenvalue; singular value; kronecker product