论文标题
数值范围等于整个复合平面的基质铅笔
Matrix pencils with the numerical range equal to the whole complex plane
论文作者
论文摘要
本文的主要目的是证明线性铅笔$λa + b $的数值范围等于$ \ m athbb {c} $，并且仅当$ 0 $属于$ a $ a $ a $ a $ a和$ b $的关节数值范围的凸壳。我们还证明，如果线性铅笔$λa + b $的数值范围等于$ \ mathbb {c} $和$ a + a^*，b + b^* \ geq 0 $，则$ a $ a $ a and $ b $具有常见的同性恋向量。此外，我们改善了描述赫米尔线性线性铅笔的经典结果。
The main purpose of this article is to show that the numerical range of a linear pencil $λA + B$ is equal to $\mathbb{C}$ if and only if $0$ belongs to the convex hull of the joint numerical range of $A$ and $B$. We also prove that if the numerical range of a linear pencil $λA + B$ is equal to $\mathbb{C}$ and $A + A^*, B + B^* \geq 0$, then $A$ and $B$ have a common isotropic vector. Moreover, we improve the classical result which describes Hermitian linear pencils.
