an:01865998
Zbl 1016.15013
Sehgal, Sudarshan; Szigeti, Jen??
Matrices over centrally \(\mathbb Z_2\)-graded rings
EN
Beitr. Algebra Geom. 43, No. 2, 399-406 (2002).
00092629
2002
j
15B33 15A24 15A75 15A09 15A15
\(\mathbb Z_2\)-graded ring; skew polynomial ring; determinant and adjoint; invariant Cayley-Hamilton identity; inverse matrix; Grassmann algebra
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.
Rodica Covaci (Cluj-Napoca)