nLab function of positive type

Definition

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

See also

• coherent product

References

• Arnold Neumaier, Introduction to coherent spaces, (arXiv:1804.01402)

• Arnold Neumaier, Coherent Quantum Physics: A Reinterpretation of the Tradition, 1st edition, De Gruyter, 2019. ISBN:9783110667295