四元数矩阵右特征值的范围估计

Location for the right eigenvalues of quaternion matrices

讨论一个n×n阶四元数矩阵的所有右特征值的范围.对已有圆盘定理的条件加以改进,从而得到对于任意一个右特征值λ,只要存在η∈[λ],且有|λ-aii|=|η-aii|,则所有右特征值都在圆盘的并集内.另外还给出了四元数矩阵的所有右特征值或者所有主对角线元素都是实数情况下的结论.数值例子说明所得定理结论对一般情况仍成立.

The location for all the right eigenvalues of a n × n quaternionic matrix is discussed.According to the Ger(s)gorin type theorem that has been given,it gets a better conclusion that for every right eigenvalue λ,all the right eigenvalues are containned in the union of the Ger(s)gorin balls if there exists a quaternion η∈ [λ] and |λ-aii | =| η-ii |.In additon,the conclusions when all the right eigenvalues or the elements of main diagonal of a quaternionic matrix are given.Finally,it gives a numerical examples to prove the conclusion to be correct in general.