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Witnessing matrix identities and proof complexity

2018
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International journal of algebra and computation
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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