论文标题
在带有双纤维化数值范围的4 x-4矩阵上
On some 4-by-4 matrices with bi-elliptical numerical ranges
论文作者
论文摘要
4 by-4矩阵$ \ begin {bmatrix}αi＆c \\ d＆βi\ end {bmatrix} $的完整描述，带有标量为2 by-2-2对角线块，为此，数值范围是两个非浓度椭圆的壳体。通过将$ c-d^*$也是身份标量倍数的领先特殊情况减少来获得的结果。在特定情况下，当$α-β$是真实或纯虚构的情况下，结果采用特别简单的形式。提供了对相互矩阵的应用。
A complete description of 4-by-4 matrices $\begin{bmatrix}αI & C \\D & βI\end{bmatrix}$, with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which $C-D^*$ also is a scalar multiple of the identity. In particular cases when in addition $α-β$ is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.
