nLab function of positive type


Given an inhabited set ZZ, a binary function f:Z×Zf:Z \times Z \to \mathbb{C} is of positive type over ZZ if for every natural number n:n:\mathbb{N} and finite list of length nn in ZZ z:Fin(n)Zz:Fin(n) \to Z, the complex linear map G: n nG:\mathbb{C}^n \to \mathbb{C}^n whose matrix representation GG' has entries G ij=f(z i,z j)G'_{ij} = f(z_i,z_j) is Hermitan and positive semidefinite.

See also


Created on July 22, 2022 at 02:16:54. See the history of this page for a list of all contributions to it.