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Matrices with zero trace as commutators of nilpotents
Authors:Donald W Robinson
Abstract:Let CFn×n have minimum polynomial m(x). Suppose C is of zero trace and m(x) splits over F. Then, except when n = 2 and m(x) = (x - c)2 or when n = 3 and m(x) = x - c)2 with c ≠ 0, there exist nilpotents A, B ∈ Fn×n such that C = AB - BA.
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