Sehgal, Sudarshan; Szigeti, Jenő Matrices over centrally \(\mathbb Z_2\)-graded rings. (English) Zbl 1016.15013 Beitr. Algebra Geom. 43, No. 2, 399-406 (2002). The authors introduce a new computational technique for \(n\times n\) matrices over a \(\mathbb{Z}_2\)-graded ring \(R=R_0\oplus R_1\) with \(R_0\subseteq Z(R)\), leading to a new concept of the determinant which can be used to derive an invariant Cayley-Hamilton identity. An explicit construction of the inverse matrix \(A^{-1}\) for any invertible \(n\times n\) matrix \(A\) over a Grassmann algebra \(E\) is also obtained. Reviewer: Rodica Covaci (Cluj-Napoca) Cited in 1 Document MSC: 15B33 Matrices over special rings (quaternions, finite fields, etc.) 15A24 Matrix equations and identities 15A75 Exterior algebra, Grassmann algebras 15A09 Theory of matrix inversion and generalized inverses 15A15 Determinants, permanents, traces, other special matrix functions Keywords:\(\mathbb Z_2\)-graded ring; skew polynomial ring; determinant and adjoint; invariant Cayley-Hamilton identity; inverse matrix; Grassmann algebra PDF BibTeX XML Cite \textit{S. Sehgal} and \textit{J. Szigeti}, Beitr. Algebra Geom. 43, No. 2, 399--406 (2002; Zbl 1016.15013) Full Text: EMIS EuDML