四元数矩阵特征值的一些估界定理

Some Estimate Theorems of the Quaternion Matrix Eigenvalues Bound

对于四元数矩阵Ａ，利用ＡＡ，Ａ＋Ａｄ两个自共轭四元数矩阵，借助于推广了的Ｒａｙｌｅｉｇｈ商给出Ａ的左（或右）特征值（总假定是存在的）的矩，实部及虚部的矩的一些上下界估计，是对复矩阵论中著名的Ｈｉｒｓｃｈ定理，Ｐｉｃｈ定理等的扩张。

For the quaternion matrix A , we make use of two self-cojugate quaternion matrix A A and A +A. By means of the generalized Regleigh division ,we expand the bounds of the module of left (right ) eigenvalue as well as the genernlization of the Hirsch and Dick theorem of complex ma- trix theory. Some results are newly obtained.