Quantum super Manin matrices

Abstract

Manin matrices are quantum linear transformations of general quantum spaces. In this paper, we study the $q$-analogue of super Manin matrices and obtain several quantum versions of classical identities, such as Jacobi's ratio theorem, Schur's complement theorem, Cayley's complementary theorem, Muir's law, Sylvester's theorem, MacMahon Master Theorem and Newton's identities.