High Quality Content by WIKIPEDIA articles! In mathematics, the Siegel upper half-space of degree n is the set of nxn symmetric matrices over the complex number field whose imaginary part is positive definite. It is named in honor of Carl Ludwig Siegel. In the case n = 1, the Siegel upper half-space is the well-known upper half-plane. In linear algebra, a positive-definite matrix is a (Hermitian) matrix which in many ways is analogous to a positive real number. The notion is closely related to a positive-definite symmetric bilinear form (or a sesquilinear form in the complex case).

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