Classical syntactic features are revisited from an algebraic perspective, recalling a traditional argument that the ±N vs. ±V distinction involves correlated, conceptually orthogonal, features, which can be represented in the algebraic format of ±1 vs. ±i complementary elements in a vectorial space. Coupled with natural assumptions about shared information (semiotic) systems, such a space, when presumed within a labeling algorithm, allows us to deduce fundamental properties of the syntax that do not follow from the presumed computation, like core selectional restrictions for lexical categories or their very presupposition in the context of a system of grammatical categories. This article suggests how that fundamental distinction can be coupled with neurophysiological realities, some of which (represented as mathematically real) can be pinpointed into punctual representations, while others (represented as mathematically complex) are, instead, fundamentally distributed. The postulated matrix mechanics amounts to a novel perspective on how to analyze syntactic neurophysiological signals.