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Feb 19, 2020 at 13:01 comment added Denis Serre @JochenGlueck. It deserves to be more known. This property is equivalent to saying that the numerical radius is a norm over ${\bf M}_n({\mathbb C})$. Even if a matrix has real entries, it is crucial to compute its numerical radius from complex vectors, not only real ones !
Feb 19, 2020 at 12:50 comment added Jochen Glueck Thank you for your answer! If I could, I would give you a second upvote for "the superiority of the complex numbers over the real ones!"
Feb 19, 2020 at 9:14 history answered Denis Serre CC BY-SA 4.0