Siegel upper half-space  In mathematics, the Siegel upper half-space of degree "g (or genus "g) (also called the Siegel upper half-plane) is the set of "g" × "g" symmetric matrices over the complex numbers whose imaginary part is positive definite. It was introduced by . In the case "g" = 1, the Siegel upper half-space is the well-known upper half-plane.