A Method to Construct Sets of Commuting Matrices
نویسندگان
چکیده
منابع مشابه
Commuting triples of matrices
The variety C(3, n) of commuting triples of n × n matrices over C is shown to be irreducible for n = 7. It had been proved that C(3, n) is reducible for n ≥ 30, but irreducible for n ≤ 6. Guralnick and Omladič have conjectured that it is reducible for n > 7.
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Let X = (xij) and Y = (yij) be generic n by n matrices and Z = XY − Y X. Let S = k[x11, . . . , xnn, y11, . . . , ynn], where k is a field, let I be the ideal generated by the entries of Z and let R = S/I . We give a conjecture on the first syzygies of I , show how these can be used to give a conjecture on the canonical module of R. Using this and the Hilbert series of I we give a conjecture on...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2013
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v5n3p1