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It is not correct to say that a nilpotent on a finite dimensional space has spectrum {0} thanks to the Jordan form, because this fact is used precisely to prove that there exists a Jordan form. Also, the definition of nilpotent can be given on any normed space, not necessarily a Hilbert one; and is interesting on Banach spaces, too. The bias on Hilbert spaces in not appropriate for a general encyclopedia. This page should be entirely rewritten, but I have no time now. Esagherardo ( talk) 11:35, 3 April 2019 (UTC) reply