Vektorkandjaid

Vektorkandjaid are a theoretical construct used in speculative mathematics to describe carriers of vectors between vector spaces. In this framework, a vektorkandja from a vector space V to another space W is a linear map T: V → W that transfers vector data between the two spaces while preserving linear structure. A collection of such carriers for various pairs of spaces forms a broader system that can be studied for patterns of transport, composition, and compatibility.

Formally, for any pair of vector spaces V and W over a common field, a vektorkandja is the data of a linear map T: V → W. When a chain of spaces is present, carriers can be composed: if T1: V → W and T2: W → U are carriers, their composite T2 ∘ T1: V → U is itself a carrier in the same framework. This composition is associative and, for each space V, the identity map id_V: V → V acts as a neutral carrier. In many treatments, vektorkandjaid are studied alongside constructions such as direct sums and tensor products, which produce new carriers from existing ones.

Examples include the identity carrier id_V on any space V, and a projection carrier P_U: V → U for a subspace U ⊆ V. More generally, any linear transformation between spaces serves as a carrier within this scheme. The concept becomes particularly useful in discussions of coordinate changes, data transport across networked vector spaces, and modeling of vector-flow through layered structures.

See also: vector space, linear map, composition, direct sum, tensor product, category theory.