Categories with Complements

Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features ±1, ±i scalars that allow for the construction a vector space, this paper studies possibility organizing 2 × square matrices. In system proposed to explore “head-complement” relations, operating yields measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical categories. Functional/grammatical deploy same albeit organized differently matrix diagonal off-diagonal. The algebraic result is group well-defined mathematical properties, properly includes Pauli standard use quantum computation. system, presumed difference between interactions—here, context head-complement sort—reduces whether magnitude eigenvalue 1 not, latter instance inducing asymmetric interactions.