Abstract
ABSTRACT We deal with the Roberts numerical radius orthogonality. In the case of 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 complex matrices. Some other related results are also discussed.
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