Sweeping words and the length of a generic vector subspace of Mn(F)
نویسندگان
چکیده
The main result of this short note is a generic version of Paz’ conjecture on the length of generating sets in matrix algebras. Consider a generic g-tuple A = (A1, . . . , Ag) of n × n matrices over an infinite field. We show that whenever g ≥ n, the set of all words of degree 2d in A spans the full n × n matrix algebra. Our proofs use generic matrices, are combinatorial and depend on the construction of special kinds of directed multigraphs with few edge-disjoint walks.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 143 شماره
صفحات -
تاریخ انتشار 2016