矩阵的特征值与矩阵方程的关系

The relationship between the eigenvalues of matrix and matrix equations

研究了矩阵A与A*的方程与A的特征值的关系.利用特征值的性质,得出了A的特征值λ应满足的条件.这个结果刻划了一些特殊矩阵的特征值的性质,并利用这个结果给出了广义投影算子的一个充要条件.

In this paper,the relationship between the equation of A and A ＊ and eigenvalue of A has been researched. By using the characteristic of eigenvalue,we get the condition that the eigenvalue λ of A may satisfy. This result has characterized the characteristic of the eigenvalue of some special matrix, and we have used this result to give a necessary and sufficient condition about generalized projections.