Graded differential geometry of graded matrix algebras

We study the graded derivation-based noncommutative differential geometry o f the Z(2)-graded algebra M(n parallel to m) of complex (n+m)x(n+m)-matrice s with the "usual block matrix grading" (for n not equal m). Beside the (in finite-dimensional) algebra of graded forms, the graded Cartan calculus, gr aded symplectic structure, graded vector bundles, graded connections and cu rvature are introduced and investigated. In particular we prove the univers ality of the graded derivation-based first-order differential calculus and show that M(n\m) is a "noncommutative graded manifold" in a stricter sense: There is a natural body map and the cohomologies of M(n\m) and its body co incide (as in the case of ordinary graded manifolds). (C) 1999 American Ins titute of Physics. [S0022-2488(99)03811-6].