ABSTRACT

We deal with the Roberts numerical radius orthogonality. In the case of $2\times 2$ complex matrices, we give some necessary and sufficient conditions for the numerical range to be symmetric by employing the Roberts orthogonality with respect to the numerical radius. In addition, we present an interrelation between the Roberts orthogonality and the Birkhoff–James orthogonality with respect to the numerical radius for $n\times n$ complex matrices. Some other related results are also discussed.

中文翻译：

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罗伯茨数值半径正交性

摘要

我们处理罗伯茨数值半径正交性。如果是$2\times 2$对于复数矩阵，我们通过利用相对于数值半径的Roberts正交性，为数值范围对称提供了一些充要条件。此外，我们提出了Roberts正交性和Birkhoff-James正交性之间关于数值半径的相互关系$ñ\times ñ$复杂矩阵。还讨论了其他一些相关结果。