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Witnessing matrix identities and proof complexity
2018
International journal of algebra and computation
We use results from the theory of algebras with polynomial identities (PI algebras) to study the witness complexity of matrix identities. A matrix identity of d × d matrices over a field F is a non-commutative polynomial f (x 1 , . . . , x n ) over F, such that f vanishes on every d × d matrix assignment to its variables. For any field F of characteristic 0, any d > 2 and any finite basis of d × d matrix identities over F, we show there exists a family of matrix identities (f n ) n∈N , such
doi:10.1142/s021819671850011x
fatcat:aevrlmha6bd5djqugsialn55fu