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of order m<, depends only on \< and, by (4.6), its (a, ß) element is a function of a -ß. If we define Ni = (e2, • • • , em; , 0), where / = (ei, ■ • • , em¡), then (4.8) Li and is a polynomial in Ni. Since J\ is also a polynomial in iV¿ it must commute with V\ The above results were derived for H 6 UHM. However, properties (ii) and (iii) generalize immediately to all Hessenberg matrices by the remarks at the beginning of Section 2.doi:10.1090/s0025-5718-1967-0223082-8 fatcat:rlkbawrq5fggpk2rdts6cmih7m