Bernik, JanezLivshits, LeoMacDonald, Gordon W.Marcoux, Laurent W.Mastnak, MitjaRadjavi, Heydar2022-05-102022-05-102021-07-20https://doi.org/10.1090/proc/15523http://hdl.handle.net/10012/18251First published in Proceedings of the American Mathematical Society in volume 149, issue 10 in 2021, published by the American Mathematical SocietyWe study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L on a Hilbert space, every principal m-dimensional ortho-compression of L has algebraic degree less than m if and only if rank(L − λI) ≤ m − 2 for some λ ∈ Censpatial matricial numerical rangesalgebraic degreerank modulo scalarsorthogonal compressionsprincipal submatricescyclic matricesnon-derogatory matricesArticle