Vektoraalseid

Vektoraalseid is a hypothetical construct in mathematics intended to generalize scalar measures to vector-valued invariants. Given a class of geometric or combinatorial objects on a fixed space, a vektoraalseid assigns to each object a vector in a fixed vector space V in a way that encodes size and orientation information beyond a single number. The term described here is hypothetical and not part of a formal standard.

Basic axioms include additivity over disjoint unions and functorial behavior with respect to structure-preserving maps. If f: X → Y is a morphism between objects, the associated map on the invariants respects composition, giving a linear relation between the vectors assigned to X and Y. Normalization conditions may fix the value on simple objects (for example, the invariant of a point equals a prescribed vector).

Examples are used in speculative or pedagogical contexts to illustrate how classical scalar invariants, such as Euler characteristic, may be extended to vector-valued settings. In naive instances, a vektoraalseid could be defined by weighting components of a standard scalar invariant or by aggregating local contributions from a decomposition.

Relation to established concepts includes vector-valued measures, K-theory, and cohomology theories with coefficients. The term is not widely standardized in published literature, and the construct remains primarily a didactic or exploratory tool rather than a canonical object. See also vector-valued measures, Euler characteristic, and characteristic classes. References are primarily textbooks and lecture notes exploring generalized invariants.