Noncommutativity Makes Determinants Hard

Abstract

We consider the complexity of computing the determinant over arbitrary finite-dimensional algebras. We first consider the case that A is fixed. We obtain the following dichotomy: If A/ radA is noncommutative, then computing the determinant over A is hard. “Hard” here means #P-hard over fields of characteristic 0 and ModpP-hard over fields of characteristic… (More)
DOI: 10.1007/978-3-642-39206-1_15

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